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    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentDescriptionOfVariableRateBasis_8e2ff85f-da43-41ef-a44b-2ac90119cb3a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentDescriptionOfVariableRateBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, basis spread on variable rate (in basis points)</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_45cdaf9b-c01f-42c8-bcba-f7d0f4713b28_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from common stock offerings</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
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    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems_9b2b7c25-183c-4ac2-9331-5e943095937c_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Controlling interest joint ventures and equity method investees [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1"/>
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    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAtCost_56b64d8d-0ec2-4604-a8d6-3ad738927fa6_totalLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Real estate, development and value-add properties</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAtCost_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, at Cost</link:label>
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    <link:label id="lab_us-gaap_RentalProperties_0e468509-2252-4ecc-b659-02ba2a176562_terseLabel_en-US" xlink:label="lab_us-gaap_RentalProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate properties</link:label>
    <link:label id="lab_us-gaap_RentalProperties_label_en-US" xlink:label="lab_us-gaap_RentalProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rental Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RentalProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RentalProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RentalProperties" xlink:to="lab_us-gaap_RentalProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_6865ba3e-fb85-4a50-bb3a-5f4c3e12a84d_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_OwnershipAxis"/>
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    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncomeLeasePayments_66383f61-eb29-4ead-bca1-dd4e1a8014ec_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncomeLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease income - operating leases</link:label>
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    <link:label id="lab_egp_Propertycapitalexpenditurespayable_86519406-81ef-4f5d-b817-2d39d74e9880_terseLabel_en-US" xlink:label="lab_egp_Propertycapitalexpenditurespayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate improvements and capitalized leasing costs payable</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_c8e06431-40b9-4a12-a6f7-7eec6e52c459_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders</link:label>
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    <link:label id="lab_egp_CompanyPerformanceBasedAwardMember_documentation_en-US" xlink:label="lab_egp_CompanyPerformanceBasedAwardMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Company performance based award</link:label>
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    <link:label id="lab_us-gaap_Land_c4face55-e857-44ab-a977-00b6eed6bdda_terseLabel_en-US" xlink:label="lab_us-gaap_Land" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_Land_label_en-US" xlink:label="lab_us-gaap_Land" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land</link:label>
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    <link:label id="lab_egp_Operatingleaseliabilitiesofficeleases_f71a14a1-dcd1-43bf-bbf1-e6f558d530e4_terseLabel_en-US" xlink:label="lab_egp_Operatingleaseliabilitiesofficeleases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities - Office leases</link:label>
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    <link:label id="lab_egp_Operatingleaseliabilitiesofficeleases_documentation_en-US" xlink:label="lab_egp_Operatingleaseliabilitiesofficeleases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating lease liabilities - office leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_Operatingleaseliabilitiesofficeleases" xlink:href="egp-20240630.xsd#egp_Operatingleaseliabilitiesofficeleases"/>
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    <link:label id="lab_egp_FairValueOfSharesGrantedAsOfTheGrantDates_63bfe7ca-0d35-4220-91fd-0fdfeb3a0c28_terseLabel_en-US" xlink:label="lab_egp_FairValueOfSharesGrantedAsOfTheGrantDates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of shares granted, as of the grant dates</link:label>
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    <link:label id="lab_us-gaap_LineOfCreditMember_ef5edff0-daac-4788-b43b-d80428554b96_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit [Member}</link:label>
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    <link:label id="lab_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock_41889371-245e-4bc3-bf62-fc13a0e50212_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasesOfLessorDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income [Text Block]</link:label>
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    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_444b9839-91a1-460d-ba32-f1042a84abdb_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and Building Improvements</link:label>
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    <link:label id="lab_us-gaap_GainLossOnCondemnation_b2b97398-9f84-4fd4-afd7-758c7db97c82_negatedLabel_en-US" xlink:label="lab_us-gaap_GainLossOnCondemnation" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Gain on involuntary conversion and business interruption claims</link:label>
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    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_b07129a1-5651-42e5-8c81-4a6b15f9ec46_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases_950404cb-a408-4c0e-8194-b94be471816c_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">In-place lease intangibles</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Acquired-in-Place Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_SaleOfStockWeightedAveragePricePerShare_2df7fd37-a4ae-4c90-9893-813405af23cc_terseLabel_en-US" xlink:label="lab_egp_SaleOfStockWeightedAveragePricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, weighted average price per share</link:label>
    <link:label id="lab_egp_SaleOfStockWeightedAveragePricePerShare_label_en-US" xlink:label="lab_egp_SaleOfStockWeightedAveragePricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of stock, weighted average price per share</link:label>
    <link:label id="lab_egp_SaleOfStockWeightedAveragePricePerShare_documentation_en-US" xlink:label="lab_egp_SaleOfStockWeightedAveragePricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of stock, weighted average price per share</link:label>
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    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock_ec83d418-65e8-47d7-accc-ec5d075257c7_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Properties</link:label>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_ccfede80-c10b-4634-8320-8c49f2b3b8fc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_50c66518-a15b-485f-a881-5f9659a4cd90_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfRevenueAbstract_894fb36b-ae35-4bd7-8d7d-dc6003ae63d2_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EXPENSES</link:label>
    <link:label id="lab_us-gaap_CostOfRevenueAbstract_label_en-US" xlink:label="lab_us-gaap_CostOfRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Revenue [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfRevenueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CostOfRevenueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfRevenueAbstract" xlink:to="lab_us-gaap_CostOfRevenueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_TotalRealEstatePropertiesAcquired_4949dade-3f44-4482-8ffb-988ea405ce9b_terseLabel_en-US" xlink:label="lab_egp_TotalRealEstatePropertiesAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total real estate properties acquired</link:label>
    <link:label id="lab_egp_TotalRealEstatePropertiesAcquired_label_en-US" xlink:label="lab_egp_TotalRealEstatePropertiesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total real estate properties acquired</link:label>
    <link:label id="lab_egp_TotalRealEstatePropertiesAcquired_documentation_en-US" xlink:label="lab_egp_TotalRealEstatePropertiesAcquired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total real estate properties acquired</link:label>
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    <link:label id="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensationForfeited_0c19e986-5d3d-4011-a382-6862d999d70b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensationForfeited" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Withheld shares of common stock to satisfy tax withholding obligations in connection with the issuance of common stock</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_c08a9d31-e918-4366-9516-da3a43b4e2f6_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES AND EQUITY</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_UseOfEstimatesTextBlock_7c7ec545-b062-4d42-94f3-9322d2239d02_terseLabel_en-US" xlink:label="lab_egp_UseOfEstimatesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">USE OF ESTIMATES</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityAbstract_8fb9f03d-eab8-4299-b369-fb034da37917_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">STOCKHOLDERS' EQUITY</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax_eccb578c-f537-4633-8879-f24da5c6ad43_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss) - interest rate swaps</link:label>
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    <link:label id="lab_us-gaap_OtherAssetsAbstract_a6e9bd24-5ba1-4dfa-94c0-04c4da7f50f0_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets [Abstract]</link:label>
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    <link:label id="lab_egp_Creditfacilityextensionoption_0f3f552f-773a-4afa-a5bd-49bcd35a5779_terseLabel_en-US" xlink:label="lab_egp_Creditfacilityextensionoption" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extension option on credit facility</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_363aa75c-a83b-4138-be8d-60c2b16b3eae_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share</link:label>
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    <link:label id="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization_c592b801-9e79-4aab-a6f2-f14667223c87_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization of acquired below market lease intangibles</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BelowMarketLeaseAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:to="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AwardRecipientTypeEmployeeMember_6f3d1c36-492c-4ae2-b135-1794d7e65fa7_terseLabel_en-US" xlink:label="lab_egp_AwardRecipientTypeEmployeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Recipient Type Employee [Member]</link:label>
    <link:label id="lab_egp_AwardRecipientTypeEmployeeMember_label_en-US" xlink:label="lab_egp_AwardRecipientTypeEmployeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Recipient Type Employee [Member]</link:label>
    <link:label id="lab_egp_AwardRecipientTypeEmployeeMember_documentation_en-US" xlink:label="lab_egp_AwardRecipientTypeEmployeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Award Recipient Type Employee [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AwardRecipientTypeEmployeeMember" xlink:href="egp-20240630.xsd#egp_AwardRecipientTypeEmployeeMember"/>
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    <link:label id="lab_egp_A75MillionInterestRateSwapExecutedIn2022Member_8191404c-8661-4468-9599-946e75030023_terseLabel_en-US" xlink:label="lab_egp_A75MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">$75 million interest rate swap executed in 2022</link:label>
    <link:label id="lab_egp_A75MillionInterestRateSwapExecutedIn2022Member_label_en-US" xlink:label="lab_egp_A75MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">$75 million interest rate swap executed in 2022 [Member]</link:label>
    <link:label id="lab_egp_A75MillionInterestRateSwapExecutedIn2022Member_documentation_en-US" xlink:label="lab_egp_A75MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">$75 million interest rate swap executed in 2022</link:label>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_63736bf4-9528-4c01-9a96-2b9639ca8494_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Borrowing Capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Current Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_dc79fbd3-2caa-41e3-9a89-d4211d3be9c9_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Amount [Member]</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesUnclassifiedAbstract_7b5b35f6-cefb-4618-9efa-2b19633d3f90_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesUnclassifiedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities, Unclassified [Abstract]</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesUnclassifiedAbstract_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesUnclassifiedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Unclassified [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesUnclassifiedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilitiesUnclassifiedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesUnclassifiedAbstract" xlink:to="lab_us-gaap_OtherLiabilitiesUnclassifiedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_658da145-b94a-468e-b40c-65638dfaf72b_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_963055e0-89d8-46e1-a43e-c9ea88b8153c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingsAndImprovementsGross_2cd08eb4-d519-40fa-9c37-199f3196dd0e_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingsAndImprovementsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and building improvements</link:label>
    <link:label id="lab_us-gaap_BuildingsAndImprovementsGross_label_en-US" xlink:label="lab_us-gaap_BuildingsAndImprovementsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Buildings and Improvements, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingsAndImprovementsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BuildingsAndImprovementsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingsAndImprovementsGross" xlink:to="lab_us-gaap_BuildingsAndImprovementsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_4dc4b049-ac1b-4cc9-86a4-7d73a3cab95e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_fb6469d2-5d8d-4e13-a6df-cec88963ea16_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_d8a5aedf-bf2e-4e65-9326-df13e5fdd4c2_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionDomain" xlink:to="lab_us-gaap_AssetAcquisitionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledPricePerShare_be353afd-2dfe-466c-9b49-b1c788f39b80_terseLabel_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, price per share</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledPricePerShare_label_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, price per share</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledPricePerShare_documentation_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, price per share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardSaleAgreementsSettledPricePerShare" xlink:href="egp-20240630.xsd#egp_ForwardSaleAgreementsSettledPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ForwardSaleAgreementsSettledPricePerShare" xlink:to="lab_egp_ForwardSaleAgreementsSettledPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_1f49f76f-58e8-4497-863c-0d7adf38211d_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardEquityOfferingsDomain_cae290b4-5c4d-4d84-a8c6-b98cd1e672c6_terseLabel_en-US" xlink:label="lab_egp_ForwardEquityOfferingsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward Equity Offerings [Domain]</link:label>
    <link:label id="lab_egp_ForwardEquityOfferingsDomain_label_en-US" xlink:label="lab_egp_ForwardEquityOfferingsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Equity Offerings [Domain]</link:label>
    <link:label id="lab_egp_ForwardEquityOfferingsDomain_documentation_en-US" xlink:label="lab_egp_ForwardEquityOfferingsDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Equity Offerings [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardEquityOfferingsDomain" xlink:href="egp-20240630.xsd#egp_ForwardEquityOfferingsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ForwardEquityOfferingsDomain" xlink:to="lab_egp_ForwardEquityOfferingsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward_2b0da4f8-a4e0-4738-956a-1a7aa7a99306_terseLabel_en-US" xlink:label="lab_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Comprehensive Income, Period Increase (Decrease)</link:label>
    <link:label id="lab_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward_label_en-US" xlink:label="lab_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accumulated Other Comprehensive Income (Loss) [Roll Forward]</link:label>
    <link:label id="lab_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward_documentation_en-US" xlink:label="lab_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward" xlink:href="egp-20240630.xsd#egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward" xlink:to="lab_egp_IncreaseDecreaseInAccumulatedOtherComprehensiveIncomeLossRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNoteTextBlock_4caae379-ce75-4d63-b13a-56b89adb0b1e_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss) Note [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:to="lab_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_037a247d-6af0-48ab-9e7e-219d7b5cf2e4_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber"/>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_27c6229f-503e-4c63-9a66-4ea63b3cecb2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_1d1e5198-bb6f-47b9-afd5-aade538dd3c9_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notional Amount of Interest Rate Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_209a4241-7b0f-4833-87ee-d9cc2cca55e9_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024 - Remainder of year</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_b19f56cd-c7c3-415b-9dd6-b38fd12c23d2_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common dividends declared - per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidCapitalized_d9507fb8-c1de-43b6-9dca-cf6411e60ee2_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidCapitalized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest capitalized</link:label>
    <link:label id="lab_us-gaap_InterestPaidCapitalized_label_en-US" xlink:label="lab_us-gaap_InterestPaidCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Capitalized, Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestPaidCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidCapitalized" xlink:to="lab_us-gaap_InterestPaidCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionEffectiveDateOfAcquisition_4fc805b0-534e-4c82-bca1-6b58381eea37_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionEffectiveDateOfAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Date Acquired</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionEffectiveDateOfAcquisition_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionEffectiveDateOfAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Effective Date of Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionEffectiveDateOfAcquisition" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionEffectiveDateOfAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionEffectiveDateOfAcquisition" xlink:to="lab_us-gaap_AssetAcquisitionEffectiveDateOfAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_NewForwardSaleAgreements_fe71ed33-6131-4e97-b0a1-c20a98553178_terseLabel_en-US" xlink:label="lab_egp_NewForwardSaleAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New forward sale agreements, shares</link:label>
    <link:label id="lab_egp_NewForwardSaleAgreements_label_en-US" xlink:label="lab_egp_NewForwardSaleAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New forward sale agreements</link:label>
    <link:label id="lab_egp_NewForwardSaleAgreements_documentation_en-US" xlink:label="lab_egp_NewForwardSaleAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New forward sale agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_NewForwardSaleAgreements" xlink:href="egp-20240630.xsd#egp_NewForwardSaleAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_NewForwardSaleAgreements" xlink:to="lab_egp_NewForwardSaleAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_e358a12a-97e9-4c87-8f9e-cf8a8af09ccb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common stock offering related costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_3651bd19-3b26-4feb-97bb-29c92de53389_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Depreciation_b5c6474a-5e69-41c0-9412-8f5a6d1b24d8_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation Expense</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_NetSalesPrice_5550bb57-ae4f-4a6c-9fed-9a2cafa6e6b3_verboseLabel_en-US" xlink:label="lab_egp_NetSalesPrice" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net sales price</link:label>
    <link:label id="lab_egp_NetSalesPrice_label_en-US" xlink:label="lab_egp_NetSalesPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net sales price</link:label>
    <link:label id="lab_egp_NetSalesPrice_documentation_en-US" xlink:label="lab_egp_NetSalesPrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gross sales price of property disposition less costs of sale.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_NetSalesPrice" xlink:href="egp-20240630.xsd#egp_NetSalesPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_NetSalesPrice" xlink:to="lab_egp_NetSalesPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_90eb4b42-aaf3-4087-947e-bed40dde4a8f_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_8e4ad764-6adb-42cd-9cde-8f7a15757dfe_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_b167be35-12a5-45e5-8160-fc355cbf3df6_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial Assets [Abstract]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Assets, Balance Sheet Groupings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:to="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2024OperatingPropertyAcquisitionsMember_eacf628b-792c-4401-b9f6-05a66e5ccc32_terseLabel_en-US" xlink:label="lab_egp_A2024OperatingPropertyAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024 Operating Property Acquisitions</link:label>
    <link:label id="lab_egp_A2024OperatingPropertyAcquisitionsMember_label_en-US" xlink:label="lab_egp_A2024OperatingPropertyAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024 Operating Property Acquisitions [Member]</link:label>
    <link:label id="lab_egp_A2024OperatingPropertyAcquisitionsMember_documentation_en-US" xlink:label="lab_egp_A2024OperatingPropertyAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024 Operating Property Acquisitions</link:label>
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    <link:label id="lab_egp_WeightedAveragePricePerShareMember_705ddc5a-de19-46c8-aaf2-b080695bc68e_terseLabel_en-US" xlink:label="lab_egp_WeightedAveragePricePerShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Price, Per share</link:label>
    <link:label id="lab_egp_WeightedAveragePricePerShareMember_label_en-US" xlink:label="lab_egp_WeightedAveragePricePerShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Price, Per share [Member]</link:label>
    <link:label id="lab_egp_WeightedAveragePricePerShareMember_documentation_en-US" xlink:label="lab_egp_WeightedAveragePricePerShareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Price, Per share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_WeightedAveragePricePerShareMember" xlink:href="egp-20240630.xsd#egp_WeightedAveragePricePerShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_WeightedAveragePricePerShareMember" xlink:to="lab_egp_WeightedAveragePricePerShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExcessStockSharesIssued_a5411623-318f-4504-97e0-dd8b66735ab4_terseLabel_en-US" xlink:label="lab_us-gaap_ExcessStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess Stock, Shares Issued</link:label>
    <link:label id="lab_us-gaap_ExcessStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_ExcessStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Excess Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExcessStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ExcessStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExcessStockSharesIssued" xlink:to="lab_us-gaap_ExcessStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTable_ff779824-658a-4637-b785-b3997d5d15b6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Properties [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Properties [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRealEstatePropertiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfRealEstatePropertiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRealEstatePropertiesTable" xlink:to="lab_us-gaap_ScheduleOfRealEstatePropertiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_126fd5f3-8547-4474-a760-b95c457688c9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Withheld shares of common stock to satisfy tax withholding obligations in connection with the vesting of restricted stock</link:label>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Decrease for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledShares_8fcdab2e-bcea-42fa-91f7-5660dfc1e576_terseLabel_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, shares</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledShares_label_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, shares</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledShares_documentation_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardSaleAgreementsSettledShares" xlink:href="egp-20240630.xsd#egp_ForwardSaleAgreementsSettledShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ForwardSaleAgreementsSettledShares" xlink:to="lab_egp_ForwardSaleAgreementsSettledShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_7738674e-845c-49d3-9f6b-76016cdb3aa1_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of dilutive securities</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:to="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1_7235f8bb-7cf7-4565-972d-1d712eac39ee_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt assumed in the purchase of real estate</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Debt Assumed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xlink:to="lab_us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_36808be6-b0aa-4888-9c96-16c20de230eb_terseLabel_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_b39179a2-f2fc-4bb4-ba2f-5499208b11d0_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingPricePerShare_50b40a5e-8974-4bf1-8778-371d16cce57e_terseLabel_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, price per share</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingPricePerShare_label_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, price per share</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingPricePerShare_documentation_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, price per share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardSaleAgreementsOutstandingPricePerShare" xlink:href="egp-20240630.xsd#egp_ForwardSaleAgreementsOutstandingPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ForwardSaleAgreementsOutstandingPricePerShare" xlink:to="lab_egp_ForwardSaleAgreementsOutstandingPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_973bf498-9b4e-4450-bbad-49e0934896d2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying amounts and fair value of financial instruments</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_6b23cb38-d3a4-4871-bbdb-db34bb3292a0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Accounts Payable and Accrued Expenses</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Payable and Accrued Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract_4b4f8936-d9ce-4d72-b06b-39e7bb2eab68_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net [Abstract]</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RealEstateInvestmentPropertyNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_6dbce5b9-24f6-443e-a52e-45ee0bb05b7b_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">INVESTING ACTIVITIES</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures_4313a51d-523b-4222-a7af-f0453feafd7f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Forfeitures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ShareBasedPaymentAwardsTypeDomain_f492bd99-a5ea-40ed-aadd-551e4e405b6d_terseLabel_en-US" xlink:label="lab_egp_ShareBasedPaymentAwardsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Based Payment Awards Type [Domain]</link:label>
    <link:label id="lab_egp_ShareBasedPaymentAwardsTypeDomain_label_en-US" xlink:label="lab_egp_ShareBasedPaymentAwardsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Based Payment Awards Type [Domain]</link:label>
    <link:label id="lab_egp_ShareBasedPaymentAwardsTypeDomain_documentation_en-US" xlink:label="lab_egp_ShareBasedPaymentAwardsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pertinent data describing and reflecting required goals pertaining to an equity-based compensation arrangement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ShareBasedPaymentAwardsTypeDomain" xlink:href="egp-20240630.xsd#egp_ShareBasedPaymentAwardsTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ShareBasedPaymentAwardsTypeDomain" xlink:to="lab_egp_ShareBasedPaymentAwardsTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_a625735c-3d66-406a-9331-3d090e9450d4_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_4ce40c72-fce5-4f60-a684-be8bc8deeffd_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_640d99f6-9c85-49bd-9bf2-866a20aff1fa_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_label_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpense" xlink:to="lab_us-gaap_InterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalDate1_353ad632-4b6c-4d52-8b36-7958f19b941c_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalDate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Date sold</link:label>
    <link:label id="lab_us-gaap_DisposalDate1_label_en-US" xlink:label="lab_us-gaap_DisposalDate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalDate1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DisposalDate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalDate1" xlink:to="lab_us-gaap_DisposalDate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_829c86e4-4cdf-46fc-8b9f-1eca26a751c5_verboseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Right of use liability, ground lease</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_3ee854d1-4e2c-4862-b931-e6924e30d9be_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_DevelopmentTextBlock_47c03b88-4a58-47fb-8582-5cb22040a9e5_verboseLabel_en-US" xlink:label="lab_egp_DevelopmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Development</link:label>
    <link:label id="lab_egp_DevelopmentTextBlock_label_en-US" xlink:label="lab_egp_DevelopmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Development [Text Block]</link:label>
    <link:label id="lab_egp_DevelopmentTextBlock_documentation_en-US" xlink:label="lab_egp_DevelopmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents certain disclosures of accounting policies and procedures around real estate development.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_DevelopmentTextBlock" xlink:href="egp-20240630.xsd#egp_DevelopmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_DevelopmentTextBlock" xlink:to="lab_egp_DevelopmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_fc5ba65f-788e-4dd2-802d-5a620797f57f_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_ec2b1940-5a4f-46e8-9076-574884a86213_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment_b3202283-ac1c-48d2-8abe-0b528ed05724_terseLabel_en-US" xlink:label="lab_us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses from real estate operations</link:label>
    <link:label id="lab_us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment_label_en-US" xlink:label="lab_us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Costs of Leased and Rented Property or Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment" xlink:to="lab_us-gaap_DirectCostsOfLeasedAndRentedPropertyOrEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue_5d2f52d7-e831-4821-9a90-c7eabc8cc273_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swap liabilities</link:label>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue_60a2cbe8-59b9-4bd9-af29-b57249828d52_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest rate cash flow hedge liabilities at fair value</link:label>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue_label_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Cash Flow Hedge Liability at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue" xlink:to="lab_us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_2a3e0081-98b8-4651-88db-4af765029ed7_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_SustainabilityPerformanceLinkedBasisPointReduction_08b26861-5eed-4d1b-bfec-529d1c0e3ae6_terseLabel_en-US" xlink:label="lab_egp_SustainabilityPerformanceLinkedBasisPointReduction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sustainability performance linked basis point reduction (in basis points)</link:label>
    <link:label id="lab_egp_SustainabilityPerformanceLinkedBasisPointReduction_label_en-US" xlink:label="lab_egp_SustainabilityPerformanceLinkedBasisPointReduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sustainability performance linked basis point reduction</link:label>
    <link:label id="lab_egp_SustainabilityPerformanceLinkedBasisPointReduction_documentation_en-US" xlink:label="lab_egp_SustainabilityPerformanceLinkedBasisPointReduction" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sustainability performance linked basis point reduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_SustainabilityPerformanceLinkedBasisPointReduction" xlink:href="egp-20240630.xsd#egp_SustainabilityPerformanceLinkedBasisPointReduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_SustainabilityPerformanceLinkedBasisPointReduction" xlink:to="lab_egp_SustainabilityPerformanceLinkedBasisPointReduction" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_IndustryDistributionCenterIiUndividedTenantMember_d0b6bc9a-c9cc-4f88-b5d8-150eae9c7038_terseLabel_en-US" xlink:label="lab_egp_IndustryDistributionCenterIiUndividedTenantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industry Distribution Center II - undivided tenant-in-common interest [Member]</link:label>
    <link:label id="lab_egp_IndustryDistributionCenterIiUndividedTenantMember_label_en-US" xlink:label="lab_egp_IndustryDistributionCenterIiUndividedTenantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industry Distribution Center II - undivided tenant [Member]</link:label>
    <link:label id="lab_egp_IndustryDistributionCenterIiUndividedTenantMember_documentation_en-US" xlink:label="lab_egp_IndustryDistributionCenterIiUndividedTenantMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Industry Distribution Center II is a real estate property in which the Company has a 50% undivided tenant-in-common interest.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_IndustryDistributionCenterIiUndividedTenantMember" xlink:href="egp-20240630.xsd#egp_IndustryDistributionCenterIiUndividedTenantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_IndustryDistributionCenterIiUndividedTenantMember" xlink:to="lab_egp_IndustryDistributionCenterIiUndividedTenantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_b9146740-ede8-4f63-9569-552be7f1ace4_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense for lease intangibles</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_41ea1b2e-5310-4ae8-8447-d4bb3c314ada_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet_ed0d7f9a-4bd6-42e1-bfc8-9556182f55d4_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Increase (Decrease), Net</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Increase (Decrease), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet" xlink:to="lab_us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_7813f51f-2b07-447b-9399-8dd1f1d96373_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A100MillionInterestRateSwapExecutedInDec2022Member_1a1343ba-50b1-4f76-9397-622ae3e9c4ff_terseLabel_en-US" xlink:label="lab_egp_A100MillionInterestRateSwapExecutedInDec2022Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap executed in November 2022</link:label>
    <link:label id="lab_egp_A100MillionInterestRateSwapExecutedInDec2022Member_label_en-US" xlink:label="lab_egp_A100MillionInterestRateSwapExecutedInDec2022Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap executed in Dec 2022 [Member]</link:label>
    <link:label id="lab_egp_A100MillionInterestRateSwapExecutedInDec2022Member_documentation_en-US" xlink:label="lab_egp_A100MillionInterestRateSwapExecutedInDec2022Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap executed in Dec 2022</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A100MillionInterestRateSwapExecutedInDec2022Member" xlink:href="egp-20240630.xsd#egp_A100MillionInterestRateSwapExecutedInDec2022Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A100MillionInterestRateSwapExecutedInDec2022Member" xlink:to="lab_egp_A100MillionInterestRateSwapExecutedInDec2022Member" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_MiramarLandMember_606af86b-64f4-4f89-a9eb-0e761ab33967_terseLabel_en-US" xlink:label="lab_egp_MiramarLandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Miramar Land [Member]</link:label>
    <link:label id="lab_egp_MiramarLandMember_label_en-US" xlink:label="lab_egp_MiramarLandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Miramar Land [Member]</link:label>
    <link:label id="lab_egp_MiramarLandMember_documentation_en-US" xlink:label="lab_egp_MiramarLandMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Miramar Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_MiramarLandMember" xlink:href="egp-20240630.xsd#egp_MiramarLandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_MiramarLandMember" xlink:to="lab_egp_MiramarLandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_89621e07-2512-4fa0-8e6f-e08b1bf89b74_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_97f65d0e-14c5-490b-a7a4-63362bfeffb6_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">CASH AND CASH EQUIVALENTS AT END OF PERIOD</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_de298075-3541-4378-8f0c-8b569922706b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization of acquired in-place lease intangibles</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_ff8a57ad-c8ff-44ac-8902-0943e8dbc87c_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_cdf2b8f8-19b0-439a-86d9-688bb8114219_totalLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_256fd2ba-4f30-4db1-809a-2295964a3c42_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of common stock, weighted average price per share</link:label>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_label_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_680ca211-9b16-4efe-b45d-37c02e855759_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, issued</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
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    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_9cd9618c-37b8-453a-9b37-170a775ccc67_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions In Excess Of Earnings</link:label>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Distributions in Excess of Net Income [Member]</link:label>
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    <link:label id="lab_egp_A2023DevelopmentLandAcquisitionsMember_61724edd-e382-4ba1-af3e-7d80fb33827d_terseLabel_en-US" xlink:label="lab_egp_A2023DevelopmentLandAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023 development land acquisitions</link:label>
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    <link:label id="lab_dei_SecurityExchangeName_35828f04-0722-4794-872e-e143fd40e981_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SecurityExchangeName"/>
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    <link:label id="lab_us-gaap_LongTermDebt_afbd2422-7cc2-4e9a-8091-7906e4a3bfd7_netLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_752e8065-8a9e-41c1-9530-36bd68b2a91c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Payment Arrangement [Policy Text Block]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_88d95233-9ad7-43d1-a9db-b805cec45346_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_bb4126c7-1da0-4f53-a04f-ac6d0767aa0c_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_7b733396-ce63-4714-a01c-c72fa99884c4_periodStartLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at Beginning of Period</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_a0e555dd-cdb7-41c8-a5b5-ea8ebf6c4630_periodEndLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at End of Period</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_0cf0a12e-85db-4457-9d15-4fa6df2eb3c6_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage"/>
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    <link:label id="lab_us-gaap_InterestRateDerivativeLiabilitiesAtFairValue_deef7073-af9e-416f-9f0f-b3c3d898cfe5_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateDerivativeLiabilitiesAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swap liabilities</link:label>
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    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_33244807-8ca2-4851-86b0-4ba8aa36b51d_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Distributions paid to stockholders (not including dividends accrued)</link:label>
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    <link:label id="lab_egp_InterchangeBusinessParkAndMetroAirportCommerceCenterMember_cd4954b7-5897-4064-af66-63a3fe93b362_verboseLabel_en-US" xlink:label="lab_egp_InterchangeBusinessParkAndMetroAirportCommerceCenterMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interchange Business Park and Metro Airport Commerce Center [Member]</link:label>
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    <link:label id="lab_us-gaap_AssetAcquisitionTable_a0aa74d9-f5d4-4a3b-8dbc-d3dae24cca0e_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Table]</link:label>
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    <link:label id="lab_srt_MaximumMember_4a5fb225-81ed-482e-b3d6-3096f018d46d_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_e0dc2377-5b64-438f-a81a-21d5bde83176_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">TOTAL COMPREHENSIVE INCOME</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_71d3a7cf-da2c-47db-a08e-64f9125ba3d2_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentType"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIOnDerivativesNetOfTax_ff743422-8e64-48c1-9eb7-4517c6bb065b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIOnDerivativesNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount of (income) loss reclassified from Accumulated other comprehensive income into interest expense</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIOnDerivativesNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIOnDerivativesNetOfTax"/>
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    <link:label id="lab_dei_EntityAddressAddressLine1_69c1b5ba-88bd-48a6-801a-defb5e1c6563_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
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    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine2"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_90011ded-4617-4ccd-8091-103425d0e2ae_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029 and beyond</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_CraigCorporateCenterMember_e182601f-84cf-4af7-9740-f2e7ef4da020_terseLabel_en-US" xlink:label="lab_egp_CraigCorporateCenterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Craig Corporate Center</link:label>
    <link:label id="lab_egp_CraigCorporateCenterMember_label_en-US" xlink:label="lab_egp_CraigCorporateCenterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Craig Corporate Center [Member]</link:label>
    <link:label id="lab_egp_CraigCorporateCenterMember_documentation_en-US" xlink:label="lab_egp_CraigCorporateCenterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Craig Corporate Center</link:label>
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    <link:label id="lab_us-gaap_DevelopmentInProcess_064d3b49-3f82-4d65-ac55-23be644549bc_verboseLabel_en-US" xlink:label="lab_us-gaap_DevelopmentInProcess" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Development and value-add properties</link:label>
    <link:label id="lab_us-gaap_DevelopmentInProcess_label_en-US" xlink:label="lab_us-gaap_DevelopmentInProcess" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Development in Process</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DevelopmentInProcess" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DevelopmentInProcess"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DevelopmentInProcess" xlink:to="lab_us-gaap_DevelopmentInProcess" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationGiven1_aae641f6-5d46-4c54-a0a4-8e9949af6b04_terseLabel_en-US" xlink:label="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationGiven1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of common shares issued, asset acquisition</link:label>
    <link:label id="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationGiven1_label_en-US" xlink:label="lab_us-gaap_OtherSignificantNoncashTransactionValueOfConsiderationGiven1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Significant Noncash Transaction, Value of Consideration Given</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_04052178-5932-4cc5-b779-33ae899ee81a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Liabilities [Abstract]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Liabilities, Balance Sheet Groupings [Abstract]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTable_4265df68-ca54-4435-8bef-b6e316003e3e_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_6ada3d31-fb5b-4ca6-b4e7-ca047254e577_verboseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stock-Based Compensation</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
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    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_45731c5f-7e16-416c-a7d0-38da58a72292_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
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    <link:label id="lab_egp_NetProceedsFromIssuanceOfCommonStock_a782b07f-3991-4748-88f4-ccddbd41b04e_terseLabel_en-US" xlink:label="lab_egp_NetProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from issuance of common stock</link:label>
    <link:label id="lab_egp_NetProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_egp_NetProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net proceeds from issuance of common stock</link:label>
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    <link:label id="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent_de2587ad-df5c-4065-84fc-7785af04fc0e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other payables and accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Other</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccountsPayableOtherCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_SummaryOfOtherLiabilitiesTableTextBlock_a7cd6311-cf28-4898-a01e-84bd5ec621f9_verboseLabel_en-US" xlink:label="lab_egp_SummaryOfOtherLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Summary of other liabilities</link:label>
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    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_482ca667-6a63-4605-9ef7-ed3281b8ca87_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_d5a220f4-ea5c-45ec-94d4-b5f7792cd4e1_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
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    <link:label id="lab_dei_Security12bTitle_559eaa29-009c-41dd-a9c9-021c55f7f542_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_b527b2c5-c46b-4b26-96ec-0c9a5875c822_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
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    <link:label id="lab_egp_IndividualPerformanceBasedAwardMember_b53a031e-2587-4645-b677-be172077e874_terseLabel_en-US" xlink:label="lab_egp_IndividualPerformanceBasedAwardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual performance based award</link:label>
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    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_a1c02971-22c0-4e71-8f61-eea7960d7069_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossTaxAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2024AcquisitionsMember_5db425d0-85d5-442c-b6bb-74001e4fca6d_terseLabel_en-US" xlink:label="lab_egp_A2024AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024 Acquisitions</link:label>
    <link:label id="lab_egp_A2024AcquisitionsMember_label_en-US" xlink:label="lab_egp_A2024AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024 Acquisitions [Member]</link:label>
    <link:label id="lab_egp_A2024AcquisitionsMember_documentation_en-US" xlink:label="lab_egp_A2024AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024 Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A2024AcquisitionsMember" xlink:href="egp-20240630.xsd#egp_A2024AcquisitionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A2024AcquisitionsMember" xlink:to="lab_egp_A2024AcquisitionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestments_ac6972cd-85c7-4c27-ae8a-ef6e4dc8f53c_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unconsolidated investment</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestments" xlink:to="lab_us-gaap_EquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseNet_03d75fef-876d-4e78-9a8f-6ecb9fb1f619_terseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired below market lease intangibles, net of accumulated amortization</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseNet_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BelowMarketLeaseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseNet" xlink:to="lab_us-gaap_BelowMarketLeaseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_EachYearOf4YearServicePeriodMember_43627294-0c91-4087-babd-e364b230bdf4_terseLabel_en-US" xlink:label="lab_egp_EachYearOf4YearServicePeriodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Each year of 4-year service period</link:label>
    <link:label id="lab_egp_EachYearOf4YearServicePeriodMember_label_en-US" xlink:label="lab_egp_EachYearOf4YearServicePeriodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Each year of 4-year service period [Member]</link:label>
    <link:label id="lab_egp_EachYearOf4YearServicePeriodMember_documentation_en-US" xlink:label="lab_egp_EachYearOf4YearServicePeriodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Each year of 4-year service period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_EachYearOf4YearServicePeriodMember" xlink:href="egp-20240630.xsd#egp_EachYearOf4YearServicePeriodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_EachYearOf4YearServicePeriodMember" xlink:to="lab_egp_EachYearOf4YearServicePeriodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount_44f1c720-a061-4abf-ba83-57e488631e62_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation costs capitalized as development costs</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Amount Capitalized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsCapitalizedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_TotalShareholderReturnMember_eacaa6cf-1cd7-47d1-8d77-6c1fce441e6b_terseLabel_en-US" xlink:label="lab_egp_TotalShareholderReturnMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total shareholder return</link:label>
    <link:label id="lab_egp_TotalShareholderReturnMember_label_en-US" xlink:label="lab_egp_TotalShareholderReturnMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total shareholder return [Member]</link:label>
    <link:label id="lab_egp_TotalShareholderReturnMember_documentation_en-US" xlink:label="lab_egp_TotalShareholderReturnMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total shareholder return</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_TotalShareholderReturnMember" xlink:href="egp-20240630.xsd#egp_TotalShareholderReturnMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_TotalShareholderReturnMember" xlink:to="lab_egp_TotalShareholderReturnMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_03795bbf-7a08-4075-aa6c-747f251dc91c_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateDisclosureTextBlock_3d580f16-4c6c-4cef-afdf-7593bd1b0b55_verboseLabel_en-US" xlink:label="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Properties</link:label>
    <link:label id="lab_us-gaap_RealEstateDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RealEstateDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateDisclosureTextBlock" xlink:to="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_ef9778f2-d30c-4d1c-a013-a6d5dfe57615_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Domain]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BalanceSheetLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationDomain" xlink:to="lab_us-gaap_BalanceSheetLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_747e3919-b7d9-4c3b-a09c-4ca0a2e84522_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Sold and Held For Sale and Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy_9c5e16da-3a2c-4d70-9a04-861a355ba1cf_verboseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy_label_en-US" xlink:label="lab_us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Subsidiaries or Other Investments, Consolidated Entities, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy" xlink:to="lab_us-gaap_ConsolidationSubsidiariesOrOtherInvestmentsConsolidatedEntitiesPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_48199b66-dc04-45c0-95e0-271469158678_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A50MillionInterestRateSwapExecutedIn2022Member_7f80ed52-e0cb-42d8-a9f2-8e682282ed1e_terseLabel_en-US" xlink:label="lab_egp_A50MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">$50 million interest rate swap executed in 2022</link:label>
    <link:label id="lab_egp_A50MillionInterestRateSwapExecutedIn2022Member_label_en-US" xlink:label="lab_egp_A50MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">$50 million interest rate swap executed in 2022 [Member]</link:label>
    <link:label id="lab_egp_A50MillionInterestRateSwapExecutedIn2022Member_documentation_en-US" xlink:label="lab_egp_A50MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">$50 million interest rate swap executed in 2022</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A50MillionInterestRateSwapExecutedIn2022Member" xlink:href="egp-20240630.xsd#egp_A50MillionInterestRateSwapExecutedIn2022Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A50MillionInterestRateSwapExecutedIn2022Member" xlink:to="lab_egp_A50MillionInterestRateSwapExecutedIn2022Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_b88a3d07-8163-4053-acad-caac2f8822ba_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsMember_79294fb1-4ea7-40c5-ba31-37d07b58ba52_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets [Member]</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsMember" xlink:to="lab_us-gaap_OtherAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_cb93e5b2-1263-468c-a53c-2a7450608b02_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvanceRent_f017002b-a4c4-4ee7-a7c8-74daf88342f0_terseLabel_en-US" xlink:label="lab_us-gaap_AdvanceRent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid rent and other deferred income</link:label>
    <link:label id="lab_us-gaap_AdvanceRent_label_en-US" xlink:label="lab_us-gaap_AdvanceRent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advance Rent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvanceRent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdvanceRent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvanceRent" xlink:to="lab_us-gaap_AdvanceRent" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_FollowingYearAfterPerformancePeriodMember_f936c3b0-ff6d-4211-bc4f-74f498846eea_terseLabel_en-US" xlink:label="lab_egp_FollowingYearAfterPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Following year after performance period</link:label>
    <link:label id="lab_egp_FollowingYearAfterPerformancePeriodMember_label_en-US" xlink:label="lab_egp_FollowingYearAfterPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Following year after performance period [Member]</link:label>
    <link:label id="lab_egp_FollowingYearAfterPerformancePeriodMember_documentation_en-US" xlink:label="lab_egp_FollowingYearAfterPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Following year after performance period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_FollowingYearAfterPerformancePeriodMember" xlink:href="egp-20240630.xsd#egp_FollowingYearAfterPerformancePeriodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_FollowingYearAfterPerformancePeriodMember" xlink:to="lab_egp_FollowingYearAfterPerformancePeriodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireLand_ddbd475d-838d-4127-bd12-cfac258d9f4a_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireLand" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to Acquire Land</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireLand_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireLand" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Land</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireLand" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireLand"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireLand" xlink:to="lab_us-gaap_PaymentsToAcquireLand" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInRetainagePayable_faa8f616-24ae-4324-a842-66c75a290134_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInRetainagePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in accrued development costs</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInRetainagePayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInRetainagePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Retainage Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInRetainagePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInRetainagePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInRetainagePayable" xlink:to="lab_us-gaap_IncreaseDecreaseInRetainagePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_4637dd0f-7fbe-4448-9a8b-df9615b354e4_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_RisksAndUncertaintiesPolicyTextBlock_77974a2d-5d8e-4776-a71e-235cdb019f96_terseLabel_en-US" xlink:label="lab_egp_RisksAndUncertaintiesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties</link:label>
    <link:label id="lab_egp_RisksAndUncertaintiesPolicyTextBlock_label_en-US" xlink:label="lab_egp_RisksAndUncertaintiesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties [Policy Text Block]</link:label>
    <link:label id="lab_egp_RisksAndUncertaintiesPolicyTextBlock_documentation_en-US" xlink:label="lab_egp_RisksAndUncertaintiesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_RisksAndUncertaintiesPolicyTextBlock" xlink:href="egp-20240630.xsd#egp_RisksAndUncertaintiesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_RisksAndUncertaintiesPolicyTextBlock" xlink:to="lab_egp_RisksAndUncertaintiesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_GrossProceedsInThousandsMember_13445f96-8975-4d8d-b04d-546a469f8d9d_terseLabel_en-US" xlink:label="lab_egp_GrossProceedsInThousandsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Proceeds, In Thousands</link:label>
    <link:label id="lab_egp_GrossProceedsInThousandsMember_label_en-US" xlink:label="lab_egp_GrossProceedsInThousandsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Proceeds, In Thousands [Member]</link:label>
    <link:label id="lab_egp_GrossProceedsInThousandsMember_documentation_en-US" xlink:label="lab_egp_GrossProceedsInThousandsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gross Proceeds, In Thousands</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_GrossProceedsInThousandsMember" xlink:href="egp-20240630.xsd#egp_GrossProceedsInThousandsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_GrossProceedsInThousandsMember" xlink:to="lab_egp_GrossProceedsInThousandsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AcquiredAboveMarketLeaseIntangibles_74d38d80-7e58-415f-8ec5-78752d79b914_terseLabel_en-US" xlink:label="lab_egp_AcquiredAboveMarketLeaseIntangibles" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired above market lease intangibles</link:label>
    <link:label id="lab_egp_AcquiredAboveMarketLeaseIntangibles_label_en-US" xlink:label="lab_egp_AcquiredAboveMarketLeaseIntangibles" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired above market lease intangibles</link:label>
    <link:label id="lab_egp_AcquiredAboveMarketLeaseIntangibles_documentation_en-US" xlink:label="lab_egp_AcquiredAboveMarketLeaseIntangibles" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the amount of value allocated by a lessor (acquirer) to lease agreements which exist at acquisition of a leased property.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AcquiredAboveMarketLeaseIntangibles" xlink:href="egp-20240630.xsd#egp_AcquiredAboveMarketLeaseIntangibles"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AcquiredAboveMarketLeaseIntangibles" xlink:to="lab_egp_AcquiredAboveMarketLeaseIntangibles" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_1384e8b9-36f3-4038-abda-f65faf30c9f0_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_26f40102-9b12-4e21-bb9a-01f49a39bc16_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives, Policy</link:label>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_236940b0-2606-47ad-a7a5-67fca819afcc_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OPERATING ACTIVITIES</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock_2d7c5899-7aad-43c8-b00e-61eac485d94c_terseLabel_en-US" xlink:label="lab_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired Assets and Assumed Liabilities [Table]</link:label>
    <link:label id="lab_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired Assets and Assumed Liabilities [Table Text Block]</link:label>
    <link:label id="lab_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock_documentation_en-US" xlink:label="lab_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquired Assets and Assumed Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock" xlink:href="egp-20240630.xsd#egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock" xlink:to="lab_egp_AcquiredAssetsAndAssumedLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_6517105e-6a93-41d8-8993-621f82c1245c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_Accountsreceivable_9d06e079-6781-431a-b2b5-6f0986985bd8_terseLabel_en-US" xlink:label="lab_egp_Accountsreceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_egp_Accountsreceivable_label_en-US" xlink:label="lab_egp_Accountsreceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_egp_Accountsreceivable_documentation_en-US" xlink:label="lab_egp_Accountsreceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_Accountsreceivable" xlink:href="egp-20240630.xsd#egp_Accountsreceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_Accountsreceivable" xlink:to="lab_egp_Accountsreceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_d87656a2-32bc-46fa-9718-f261cfe94c31_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, outstanding</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome_63f1ed74-b12f-47c3-8384-2b8cfe07c0ca_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions in excess of earning</link:label>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome_label_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Distributions in Excess of Net Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedDistributionsInExcessOfNetIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:to="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_078f340c-8d91-4c06-a985-df44732697d9_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">BASIC PER COMMON SHARE DATA FOR NET INCOME ATTRIBUTABLE TO EASTGROUP PROPERTIES, INC. COMMON STOCKHOLDERS</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_fc12cb91-8f98-48eb-8b6e-2cd00cd5167a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BASIC EPS COMPUTATION FOR NET INCOME AVAILABLE TO EASTGROUP PROPERTIES, INC. COMMON STOCKHOLDERS [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments_c1c1aa05-0be4-4060-a761-57d6b815e002_verboseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss) - interest rate swaps</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Cash Flow Hedging Instruments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments" xlink:to="lab_us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromUnsecuredLinesOfCredit_6217335b-ff87-4bc7-a242-171bb5716167_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromUnsecuredLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from unsecured bank credit facilities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromUnsecuredLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_ProceedsFromUnsecuredLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Unsecured Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromUnsecuredLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromUnsecuredLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromUnsecuredLinesOfCredit" xlink:to="lab_us-gaap_ProceedsFromUnsecuredLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOperatingActivitiesCashFlowStatement_254419de-1ae1-4da5-9901-f33410ad130e_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherOperatingActivitiesCashFlowStatement" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherOperatingActivitiesCashFlowStatement_label_en-US" xlink:label="lab_us-gaap_OtherOperatingActivitiesCashFlowStatement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Activities, Cash Flow Statement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingActivitiesCashFlowStatement" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherOperatingActivitiesCashFlowStatement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOperatingActivitiesCashFlowStatement" xlink:to="lab_us-gaap_OtherOperatingActivitiesCashFlowStatement" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2023DevelopmentLandDispositionsMember_f6407207-fbc5-482e-8a14-5e7be98c38ee_terseLabel_en-US" xlink:label="lab_egp_A2023DevelopmentLandDispositionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023 development land dispositions</link:label>
    <link:label id="lab_egp_A2023DevelopmentLandDispositionsMember_label_en-US" xlink:label="lab_egp_A2023DevelopmentLandDispositionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2023 development land dispositions [Member]</link:label>
    <link:label id="lab_egp_A2023DevelopmentLandDispositionsMember_documentation_en-US" xlink:label="lab_egp_A2023DevelopmentLandDispositionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2023 development land dispositions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A2023DevelopmentLandDispositionsMember" xlink:href="egp-20240630.xsd#egp_A2023DevelopmentLandDispositionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A2023DevelopmentLandDispositionsMember" xlink:to="lab_egp_A2023DevelopmentLandDispositionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_86e8b5c0-6cb5-4c96-b1f1-ff8dd041a2ff_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_4dd3f9d6-228c-44d5-b23c-7548dc5b6997_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_8accec6f-0b39-48e1-aa34-64ac5161b2e1_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">NET CASH USED IN INVESTING ACTIVITIES</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseGross_dcd00277-164c-4a81-ab4f-83b881d3c0fa_terseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Below market lease intangibles</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseGross_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BelowMarketLeaseGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseGross" xlink:to="lab_us-gaap_BelowMarketLeaseGross" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_DirectCommonStockIssuanceActivityTableTextBlock_124d2303-fc43-47cc-a311-a35d3267e5a6_terseLabel_en-US" xlink:label="lab_egp_DirectCommonStockIssuanceActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct Common Stock Issuance Activity</link:label>
    <link:label id="lab_egp_DirectCommonStockIssuanceActivityTableTextBlock_label_en-US" xlink:label="lab_egp_DirectCommonStockIssuanceActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Common Stock Issuance Activity [Table Text Block]</link:label>
    <link:label id="lab_egp_DirectCommonStockIssuanceActivityTableTextBlock_documentation_en-US" xlink:label="lab_egp_DirectCommonStockIssuanceActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Direct Common Stock Issuance Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_DirectCommonStockIssuanceActivityTableTextBlock" xlink:href="egp-20240630.xsd#egp_DirectCommonStockIssuanceActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_DirectCommonStockIssuanceActivityTableTextBlock" xlink:to="lab_egp_DirectCommonStockIssuanceActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_9db24469-ef7e-44f3-bdbe-d3137d2ecc69_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">NET INCOME ATTRIBUTABLE TO EASTGROUP PROPERTIES, INC. COMMON STOCKHOLDERS</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_28a2f965-7d73-470d-bfa6-f32a435331af_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateSwapMember_039d5858-d6fa-4c30-a17c-fbb025bfc465_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
    <link:label id="lab_us-gaap_InterestRateSwapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestRateSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateSwapMember" xlink:to="lab_us-gaap_InterestRateSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_LEGALMATTERSAbstract_0e21fc48-e865-43f9-909a-1ff5c4622de8_terseLabel_en-US" xlink:label="lab_egp_LEGALMATTERSAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LEGAL MATTERS [Abstract]</link:label>
    <link:label id="lab_egp_LEGALMATTERSAbstract_label_en-US" xlink:label="lab_egp_LEGALMATTERSAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">LEGAL MATTERS [Abstract]</link:label>
    <link:label id="lab_egp_LEGALMATTERSAbstract_documentation_en-US" xlink:label="lab_egp_LEGALMATTERSAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">LEGAL MATTERS [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_LEGALMATTERSAbstract" xlink:href="egp-20240630.xsd#egp_LEGALMATTERSAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_LEGALMATTERSAbstract" xlink:to="lab_egp_LEGALMATTERSAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_NewForwardSaleAgreementsPricePerShare_5809f917-47d2-4e30-96d5-9badb63b5927_terseLabel_en-US" xlink:label="lab_egp_NewForwardSaleAgreementsPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New forward sale agreements, price per share</link:label>
    <link:label id="lab_egp_NewForwardSaleAgreementsPricePerShare_label_en-US" xlink:label="lab_egp_NewForwardSaleAgreementsPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New forward sale agreements, price per share</link:label>
    <link:label id="lab_egp_NewForwardSaleAgreementsPricePerShare_documentation_en-US" xlink:label="lab_egp_NewForwardSaleAgreementsPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New forward sale agreements, price per share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_NewForwardSaleAgreementsPricePerShare" xlink:href="egp-20240630.xsd#egp_NewForwardSaleAgreementsPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_NewForwardSaleAgreementsPricePerShare" xlink:to="lab_egp_NewForwardSaleAgreementsPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_ada95284-78ce-46b5-b642-9f56951ebb4b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_LosAngelesCorporateCenterMember_d1322979-21a2-4d35-92af-5f9c6865a195_terseLabel_en-US" xlink:label="lab_egp_LosAngelesCorporateCenterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Los Angeles Corporate Center</link:label>
    <link:label id="lab_egp_LosAngelesCorporateCenterMember_label_en-US" xlink:label="lab_egp_LosAngelesCorporateCenterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Los Angeles Corporate Center [Member]</link:label>
    <link:label id="lab_egp_LosAngelesCorporateCenterMember_documentation_en-US" xlink:label="lab_egp_LosAngelesCorporateCenterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Los Angeles Corporate Center</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_LosAngelesCorporateCenterMember" xlink:href="egp-20240630.xsd#egp_LosAngelesCorporateCenterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_LosAngelesCorporateCenterMember" xlink:to="lab_egp_LosAngelesCorporateCenterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_1b988473-59f6-496f-b73d-e866d3f65781_terseLabel_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name of Property [Domain]</link:label>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_label_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Name of Property [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:to="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_PelzerPointCommerceCenter1Member_862e1358-1919-4b2f-8fe3-3fcf675821a6_terseLabel_en-US" xlink:label="lab_egp_PelzerPointCommerceCenter1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pelzer Point Commerce Center 1</link:label>
    <link:label id="lab_egp_PelzerPointCommerceCenter1Member_label_en-US" xlink:label="lab_egp_PelzerPointCommerceCenter1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pelzer Point Commerce Center 1 [Member]</link:label>
    <link:label id="lab_egp_PelzerPointCommerceCenter1Member_documentation_en-US" xlink:label="lab_egp_PelzerPointCommerceCenter1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pelzer Point Commerce Center 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_PelzerPointCommerceCenter1Member" xlink:href="egp-20240630.xsd#egp_PelzerPointCommerceCenter1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_PelzerPointCommerceCenter1Member" xlink:to="lab_egp_PelzerPointCommerceCenter1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2023AcquisitionsMember_b52792c9-44fc-4f29-a167-5a093897ffbe_terseLabel_en-US" xlink:label="lab_egp_A2023AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023 Acquisitions</link:label>
    <link:label id="lab_egp_A2023AcquisitionsMember_label_en-US" xlink:label="lab_egp_A2023AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2023 Acquisitions [Member]</link:label>
    <link:label id="lab_egp_A2023AcquisitionsMember_documentation_en-US" xlink:label="lab_egp_A2023AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2023 Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A2023AcquisitionsMember" xlink:href="egp-20240630.xsd#egp_A2023AcquisitionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A2023AcquisitionsMember" xlink:to="lab_egp_A2023AcquisitionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentsAbstract_9eda2291-e6a8-4df9-a8d2-05f399c9bac5_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Properties</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investments, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RealEstateInvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentsAbstract" xlink:to="lab_us-gaap_RealEstateInvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_a71be3cf-d2db-46f4-9537-0d59f542a661_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract_7b49cb75-71f3-46ba-8175-3e1597b5e38b_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Expenses [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_15a2ddc5-6f19-4ea9-b792-a983824e65b9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-term Debt [Table Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
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    <link:label id="lab_us-gaap_Liabilities_cb539c9b-ad3c-43c6-80e7-d19ae42140bc_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_709d942a-edac-46d0-9a13-46a84eaf034f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of total shares granted, forfeited and delivered</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Activity [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_AssetAcquisitionAxis_cf0af365-d4e8-444c-961f-51eb0c4eb0a2_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionAxis"/>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_caf34548-a72e-4482-a848-5528ee19db81_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Consideration</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration"/>
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    <link:label id="lab_us-gaap_VestingDomain_cbb4a6b4-3027-4119-8f5a-0e9d1732efdd_terseLabel_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:label id="lab_us-gaap_VestingDomain_label_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VestingDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingDomain" xlink:to="lab_us-gaap_VestingDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_c5d5cb02-8294-488f-b317-ca50d30c13a2_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetRelatedDisclosuresAbstract_c34e7967-23b5-4afc-95b6-6770d184bf62_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetRelatedDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BALANCE SHEET PARENTHETICAL DISCLOSURES</link:label>
    <link:label id="lab_us-gaap_BalanceSheetRelatedDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_BalanceSheetRelatedDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Balance Sheet Related Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetRelatedDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BalanceSheetRelatedDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetRelatedDisclosuresAbstract" xlink:to="lab_us-gaap_BalanceSheetRelatedDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_99346b36-5bd2-4115-9bb7-48b5f538ac5f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate properties sold</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_a9a80e8d-b857-400f-8857-fd6d307e9749_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_080daa80-c700-413d-a6cc-9cdff2add07e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ContinuingEmployementAwardsMember_ca09c788-1fb6-43e2-b786-2923084ba820_terseLabel_en-US" xlink:label="lab_egp_ContinuingEmployementAwardsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Continuing employment awards</link:label>
    <link:label id="lab_egp_ContinuingEmployementAwardsMember_label_en-US" xlink:label="lab_egp_ContinuingEmployementAwardsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Continuing employement awards [Member]</link:label>
    <link:label id="lab_egp_ContinuingEmployementAwardsMember_documentation_en-US" xlink:label="lab_egp_ContinuingEmployementAwardsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Continuing employement awards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ContinuingEmployementAwardsMember" xlink:href="egp-20240630.xsd#egp_ContinuingEmployementAwardsMember"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_3245236b-a02b-46ca-8fb5-6f0fb03fe6d0_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AwardRecipientTypeDomain_e841f0c5-a350-45d4-865d-7e2f6c44ae8d_terseLabel_en-US" xlink:label="lab_egp_AwardRecipientTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Recipient Type [Domain]</link:label>
    <link:label id="lab_egp_AwardRecipientTypeDomain_label_en-US" xlink:label="lab_egp_AwardRecipientTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Recipient Type [Domain]</link:label>
    <link:label id="lab_egp_AwardRecipientTypeDomain_documentation_en-US" xlink:label="lab_egp_AwardRecipientTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Award Recipient Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareAbstract_2b0b9308-f1c7-4731-a8f8-4cef69c16a06_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
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    <link:label id="lab_us-gaap_BasisOfAccounting_label_en-US" xlink:label="lab_us-gaap_BasisOfAccounting" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting [Text Block]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventLineItems_e3b4dda8-cf7c-4953-84f5-81929554def8_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_9defd95e-3214-4adf-b516-2315cbb64b6d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares; $.0001 par value; 70,000,000 shares authorized; 48,652,525 shares issued and outstanding at June 30, 2024 and 47,700,432 at December 31, 2023</link:label>
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    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_4aa0e79a-edb4-4fb9-9912-f095afd2bf42_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
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    <link:label id="lab_us-gaap_LoansAssumed1_365e001c-7d71-4c7b-acb1-d2683844a52d_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAssumed1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of loans ssumed, asset acquisition</link:label>
    <link:label id="lab_us-gaap_LoansAssumed1_label_en-US" xlink:label="lab_us-gaap_LoansAssumed1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Assumed</link:label>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
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    <link:label id="lab_us-gaap_LegalMattersAndContingenciesTextBlock_103e22e7-966a-40ca-bf42-d0d6192d69d3_terseLabel_en-US" xlink:label="lab_us-gaap_LegalMattersAndContingenciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Matters and Contingencies [Text Block]</link:label>
    <link:label id="lab_us-gaap_LegalMattersAndContingenciesTextBlock_label_en-US" xlink:label="lab_us-gaap_LegalMattersAndContingenciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Matters and Contingencies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LegalMattersAndContingenciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LegalMattersAndContingenciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LegalMattersAndContingenciesTextBlock" xlink:to="lab_us-gaap_LegalMattersAndContingenciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForCapitalImprovements_2c1d42b2-dcfc-4e1a-922c-c1afc2ff7a5f_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForCapitalImprovements" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Real estate improvements</link:label>
    <link:label id="lab_us-gaap_PaymentsForCapitalImprovements_label_en-US" xlink:label="lab_us-gaap_PaymentsForCapitalImprovements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Capital Improvements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForCapitalImprovements" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsForCapitalImprovements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForCapitalImprovements" xlink:to="lab_us-gaap_PaymentsForCapitalImprovements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract"/>
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    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_5e5c9261-560e-41e8-b369-a889e50dd431_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable_17bf9392-425e-42f5-98f6-a2c057b7c29d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiaries [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Subsidiary or Equity Method Investee [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:to="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMinimum_e96eedee-1c10-4548-a05b-a796104a96bb_terseLabel_en-US" xlink:label="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMinimum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other Than Options, Potential Grants in Future Period (minimum)</link:label>
    <link:label id="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMinimum_label_en-US" xlink:label="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMinimum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other Than Options, Potential Grants in Future Period (minimum)</link:label>
    <link:label id="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMinimum_documentation_en-US" xlink:label="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMinimum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The minimum number of shares to be granted in a future period on other than stock option plans.</link:label>
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    <link:label id="lab_egp_Operatingleaseliabilitiesgroundleases_230f0332-4b5d-4f17-bcdf-615eaf742b18_terseLabel_en-US" xlink:label="lab_egp_Operatingleaseliabilitiesgroundleases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities - Ground leases</link:label>
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    <link:label id="lab_egp_Operatingleaseliabilitiesgroundleases_documentation_en-US" xlink:label="lab_egp_Operatingleaseliabilitiesgroundleases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating lease liabilities - ground leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_Operatingleaseliabilitiesgroundleases" xlink:href="egp-20240630.xsd#egp_Operatingleaseliabilitiesgroundleases"/>
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    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_6954c97c-733d-49c6-8f89-9cad093ed577_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUPPLEMENTAL CASH FLOW INFORMATION</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrentAndNoncurrent_0fb0d810-9ccc-44b7-9974-f0cff83c356f_terseLabel_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property taxes payable</link:label>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrual for Taxes Other than Income Taxes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrentAndNoncurrent"/>
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    <link:label id="lab_dei_EntityFilerCategory_2e2d4f6a-0fc7-4062-a8ca-6bfcb11295cc_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFilerCategory"/>
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    <link:label id="lab_us-gaap_OtherLiabilities_e20b05e1-24a5-4701-b01b-330c29005f05_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_6ccffdfe-32a3-4be9-bd86-81acd8fd45f4_totalLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_105206e4-b58a-4b08-8e1e-677e129ffa3e_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable"/>
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    <link:label id="lab_dei_CurrentFiscalYearEndDate_63497904-9ad9-4ef4-b354-00e22c150360_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
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    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_955b05fd-6a61-4fbf-8201-a52f07db379d_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment_3a379642-9ba2-42ee-ab60-ad0db7fb443b_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from sales of real estate investments and non-operating real estate</link:label>
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    <link:label id="lab_egp_ForwardEquityOfferingActivityTableTextBlock_d02bc8f1-03f0-49cd-a029-afe58c0a3a79_terseLabel_en-US" xlink:label="lab_egp_ForwardEquityOfferingActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward Equity Offering Activity</link:label>
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    <link:label id="lab_egp_RetainagePayable_label_en-US" xlink:label="lab_egp_RetainagePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retainage payable</link:label>
    <link:label id="lab_egp_RetainagePayable_documentation_en-US" xlink:label="lab_egp_RetainagePayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Retainage payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_RetainagePayable" xlink:href="egp-20240630.xsd#egp_RetainagePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_RetainagePayable" xlink:to="lab_egp_RetainagePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract_6a844cc9-0a59-4bd1-aa83-9eb13a97f45d_terseLabel_en-US" xlink:label="lab_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DERIVATIVE INSTRUMENTS AND HEDGING ACTIVITIES [Abstract]</link:label>
    <link:label id="lab_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract_label_en-US" xlink:label="lab_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DERIVATIVE INSTRUMENTS AND HEDGING ACTIVITIES [Abstract]</link:label>
    <link:label id="lab_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract_documentation_en-US" xlink:label="lab_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">DERIVATIVE INSTRUMENTS AND HEDGING ACTIVITIES [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract" xlink:href="egp-20240630.xsd#egp_DerivativeInstrumentsAndHedgingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract" xlink:to="lab_egp_DerivativeInstrumentsAndHedgingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_5b05dbad-0a8a-46e0-97f3-bcbdeb0f809d_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from involuntary conversion on real estate assets</link:label>
    <link:label id="lab_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Insurance Settlement, Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromInsuranceSettlementInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:to="lab_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_68bb681e-a74d-4e38-8f2f-90af2ccc5b88_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue_368d8d61-03b4-439f-92ff-6fc3a1423e29_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swap assets</link:label>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue_a8296eda-ccd6-42c0-8463-f4041f64aa33_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Cash Flow Hedge Assets at Fair Value</link:label>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue_label_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Cash Flow Hedge Asset at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestRateCashFlowHedgeAssetAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue" xlink:to="lab_us-gaap_InterestRateCashFlowHedgeAssetAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1_01bf44da-3e7f-4b42-abf2-2ea8a5dc8461_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Noncash Financial or Equity Instrument Consideration, Common Shares Issued</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Noncash Financial or Equity Instrument Consideration, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1" xlink:to="lab_us-gaap_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationSharesIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_NewForwardSaleAgreementsValue_3f256dc0-6d37-44df-a3b8-d15d7c9b97f5_terseLabel_en-US" xlink:label="lab_egp_NewForwardSaleAgreementsValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New forward sale agreements, value</link:label>
    <link:label id="lab_egp_NewForwardSaleAgreementsValue_label_en-US" xlink:label="lab_egp_NewForwardSaleAgreementsValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New forward sale agreements, value</link:label>
    <link:label id="lab_egp_NewForwardSaleAgreementsValue_documentation_en-US" xlink:label="lab_egp_NewForwardSaleAgreementsValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New forward sale agreements, value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_NewForwardSaleAgreementsValue" xlink:href="egp-20240630.xsd#egp_NewForwardSaleAgreementsValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_NewForwardSaleAgreementsValue" xlink:to="lab_egp_NewForwardSaleAgreementsValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_712a5308-76e2-4fb3-a454-1c96dabb138d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TenantImprovements_6900d2c2-2f9b-4e09-8b1c-7bb33fd871e8_terseLabel_en-US" xlink:label="lab_us-gaap_TenantImprovements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tenant and other improvements</link:label>
    <link:label id="lab_us-gaap_TenantImprovements_label_en-US" xlink:label="lab_us-gaap_TenantImprovements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tenant Improvements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TenantImprovements" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TenantImprovements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TenantImprovements" xlink:to="lab_us-gaap_TenantImprovements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_01e6f2e5-b3ca-4b7b-83d4-d15801d02c5e_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Grant date fair value of shares issued (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainOnSaleOfInvestments_4ca86d19-1831-43cc-9d73-918a3ab70867_terseLabel_en-US" xlink:label="lab_us-gaap_GainOnSaleOfInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale of non-operating real estate</link:label>
    <link:label id="lab_us-gaap_GainOnSaleOfInvestments_label_en-US" xlink:label="lab_us-gaap_GainOnSaleOfInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain on Sale of Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainOnSaleOfInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainOnSaleOfInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainOnSaleOfInvestments" xlink:to="lab_us-gaap_GainOnSaleOfInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingMember_e8db792c-cc18-4296-ac8c-9b7bf8b29d2c_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingMember" xlink:to="lab_us-gaap_BuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidInsurance_e6e991af-61f9-4108-934b-d4bc193c6c1d_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidInsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid Insurance</link:label>
    <link:label id="lab_us-gaap_PrepaidInsurance_label_en-US" xlink:label="lab_us-gaap_PrepaidInsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidInsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PrepaidInsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidInsurance" xlink:to="lab_us-gaap_PrepaidInsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A100MillionInterestRateSwapExecutedIn2022Member_c61daf8a-14c2-4cc2-ac1a-57fb7354a796_terseLabel_en-US" xlink:label="lab_egp_A100MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap executed in 2022</link:label>
    <link:label id="lab_egp_A100MillionInterestRateSwapExecutedIn2022Member_label_en-US" xlink:label="lab_egp_A100MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap executed in 2022 [Member]</link:label>
    <link:label id="lab_egp_A100MillionInterestRateSwapExecutedIn2022Member_documentation_en-US" xlink:label="lab_egp_A100MillionInterestRateSwapExecutedIn2022Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap executed in 2022</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A100MillionInterestRateSwapExecutedIn2022Member" xlink:href="egp-20240630.xsd#egp_A100MillionInterestRateSwapExecutedIn2022Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A100MillionInterestRateSwapExecutedIn2022Member" xlink:to="lab_egp_A100MillionInterestRateSwapExecutedIn2022Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_964a5600-620c-4178-a141-2b1591368daf_verboseLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:label id="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_MarketableSecuritiesLineItems_2dc2970f-afa5-4226-93ee-0eec4367367f_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Offerings [Line Items]</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MarketableSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesLineItems" xlink:to="lab_us-gaap_MarketableSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledValue_98c4ef6d-24ff-4f76-a3e7-ed5cecb5f906_terseLabel_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, gross proceeds</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledValue_label_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, value</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsSettledValue_documentation_en-US" xlink:label="lab_egp_ForwardSaleAgreementsSettledValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardSaleAgreementsSettledValue" xlink:href="egp-20240630.xsd#egp_ForwardSaleAgreementsSettledValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ForwardSaleAgreementsSettledValue" xlink:to="lab_egp_ForwardSaleAgreementsSettledValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_475a8b62-ccdf-4b52-9d97-38b6460e01d6_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">NET CASH PROVIDED BY OPERATING ACTIVITIES</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
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    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingValue_31ea84e3-574a-4c8d-99f6-877872249871_terseLabel_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, value</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingValue_label_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, value</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingValue_documentation_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardSaleAgreementsOutstandingValue" xlink:href="egp-20240630.xsd#egp_ForwardSaleAgreementsOutstandingValue"/>
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    <link:label id="lab_us-gaap_AreaOfLand_cfadd73d-92f2-4ba4-b6c5-9acd63ae6b0a_terseLabel_en-US" xlink:label="lab_us-gaap_AreaOfLand" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acres of real estate investment property</link:label>
    <link:label id="lab_us-gaap_AreaOfLand_label_en-US" xlink:label="lab_us-gaap_AreaOfLand" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Area of Land</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AreaOfLand" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AreaOfLand"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AreaOfLand" xlink:to="lab_us-gaap_AreaOfLand" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebt_1dbb17f9-7535-49b4-8965-5d59eec9a9e3_verboseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt, net of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebt_f0c8ea8e-ace7-4f53-9b41-704908ffea40_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UnsecuredDebt"/>
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    <link:label id="lab_us-gaap_DeferredCostsLeasingNet_8ea8933d-b4ac-4e54-be26-0f4b8bc08d5f_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Leasing costs (principally commissions), net of accumulated amortization</link:label>
    <link:label id="lab_us-gaap_DeferredCostsLeasingNet_label_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Leasing, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsLeasingNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredCostsLeasingNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsLeasingNet" xlink:to="lab_us-gaap_DeferredCostsLeasingNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_d64ff844-c19d-4da1-ab33-f258a998d46f_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_20d712d0-6b00-445b-a088-d5b99ce09f9b_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_8e875c54-e34a-49f8-84d1-09e109eeeb61_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasesIncomeStatementLeaseRevenueAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingLeasesIncomeStatementLeaseRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Leases, Income Statement, Lease Revenue [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasesIncomeStatementLeaseRevenueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeasesIncomeStatementLeaseRevenueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasesIncomeStatementLeaseRevenueAbstract" xlink:to="lab_us-gaap_OperatingLeasesIncomeStatementLeaseRevenueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_WorldHouston23Member_149948d3-d5ae-4607-a54f-2af4b7f7c2bd_terseLabel_en-US" xlink:label="lab_egp_WorldHouston23Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">World Houston 23</link:label>
    <link:label id="lab_egp_WorldHouston23Member_label_en-US" xlink:label="lab_egp_WorldHouston23Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">World Houston 23 [Member]</link:label>
    <link:label id="lab_egp_WorldHouston23Member_documentation_en-US" xlink:label="lab_egp_WorldHouston23Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">World Houston 23</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_WorldHouston23Member" xlink:href="egp-20240630.xsd#egp_WorldHouston23Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_WorldHouston23Member" xlink:to="lab_egp_WorldHouston23Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_89210325-9eac-4b4c-8923-db145b9b47dd_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock [Member]</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_45e399b1-2a58-4dcf-8afa-f9dbbe123f18_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ATMProgramOctober2023Member_7906963a-ac63-4bbc-8959-16162909e945_terseLabel_en-US" xlink:label="lab_egp_ATMProgramOctober2023Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ATM Program - October 2023</link:label>
    <link:label id="lab_egp_ATMProgramOctober2023Member_label_en-US" xlink:label="lab_egp_ATMProgramOctober2023Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ATM Program - October 2023 [Member]</link:label>
    <link:label id="lab_egp_ATMProgramOctober2023Member_documentation_en-US" xlink:label="lab_egp_ATMProgramOctober2023Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">ATM Program - October 2023</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ATMProgramOctober2023Member" xlink:href="egp-20240630.xsd#egp_ATMProgramOctober2023Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ATMProgramOctober2023Member" xlink:to="lab_egp_ATMProgramOctober2023Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_16651b77-501b-4fd1-92db-bd2a0e87e582_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A100millioninterestrateswap2019Domain_fcfdcde6-9ed2-4d41-978f-dced5c38a4d6_terseLabel_en-US" xlink:label="lab_egp_A100millioninterestrateswap2019Domain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap (2019) [Domain]</link:label>
    <link:label id="lab_egp_A100millioninterestrateswap2019Domain_label_en-US" xlink:label="lab_egp_A100millioninterestrateswap2019Domain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap (2019) [Domain]</link:label>
    <link:label id="lab_egp_A100millioninterestrateswap2019Domain_documentation_en-US" xlink:label="lab_egp_A100millioninterestrateswap2019Domain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap (2019)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A100millioninterestrateswap2019Domain" xlink:href="egp-20240630.xsd#egp_A100millioninterestrateswap2019Domain"/>
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    <link:label id="lab_us-gaap_SubsequentEventsAbstract_0142403b-03f5-469e-8f6a-bd75a2e5419d_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtByMaturityAbstract_8dda3589-478f-4cd3-a1b7-d16f4cdc0fa6_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtByMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments of principal over future years [Abstract]</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_d599d762-c34a-4fae-8c0a-7b1117cf3bbc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement, Policy [Policy Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_76478971-b7af-4653-b9da-e2303ca13201_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OtherAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_OtherAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ExcessStockSharesAuthorized_90538dc5-b35e-4746-9423-4f183c14ffc2_terseLabel_en-US" xlink:label="lab_us-gaap_ExcessStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess shares, authorized</link:label>
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    <link:label id="lab_us-gaap_CommonStockOtherValueOutstanding_3d23cb8f-e434-4981-88b5-d0a1abe3840d_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockOtherValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Excess shares; $.0001 par value; 30,000,000 shares authorized; zero shares issued</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_473da374-cd6d-4435-bf26-3072d46e3612_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
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    <link:label id="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation_45ec8620-0f9e-41df-a5bf-74cd86f4959e_terseLabel_en-US" xlink:label="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation, net of forfeitures</link:label>
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    <link:label id="lab_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy_d0801049-4bf4-47d8-b36f-a5ddcca02e19_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Development</link:label>
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    <link:label id="lab_dei_CityAreaCode_a3f72c29-e474-40a1-9455-ad4f2d8c1bcb_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_ab8e8acc-1018-48a6-8ce7-4362fa2e578c_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_5fd6337b-96fe-4ad0-8fd5-ba97b6280c0b_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Earnings per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2023DispositionsMember_04a42d01-b66e-4a36-8128-128ca2d4b421_terseLabel_en-US" xlink:label="lab_egp_A2023DispositionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023 dispositions</link:label>
    <link:label id="lab_egp_A2023DispositionsMember_label_en-US" xlink:label="lab_egp_A2023DispositionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2023 dispositions [Member]</link:label>
    <link:label id="lab_egp_A2023DispositionsMember_documentation_en-US" xlink:label="lab_egp_A2023DispositionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2023 dispositions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A2023DispositionsMember" xlink:href="egp-20240630.xsd#egp_A2023DispositionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A2023DispositionsMember" xlink:to="lab_egp_A2023DispositionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_b28bf3c6-51b4-4385-bcb0-ae65721e877b_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Repayments on secured debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RepaymentsOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:to="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_8129af7a-f1dc-4ad7-a617-43d04c2fb701_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, ownership percentage</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_f803a6e2-7c76-43b2-a315-6f27b1461c6e_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecuritiesTable_c3b8585b-e907-4078-a2af-b7251f083653_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marketable Securities [Table]</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesTable_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MarketableSecuritiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesTable" xlink:to="lab_us-gaap_MarketableSecuritiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConstructionPayableCurrentAndNoncurrent_19622337-c62e-4f06-9e3e-b5fe113e8b81_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Development costs payable</link:label>
    <link:label id="lab_us-gaap_ConstructionPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_ConstructionPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConstructionPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ConstructionPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_ConstructionPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_cb97029c-8692-4265-afb6-2d8246d84744_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_0eb3c92a-559d-4ba7-a932-cb1f9a81d470_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">BALANCE</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_f06252e5-987d-403f-86af-3a4c48af7224_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">BALANCE</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_4f6f86b9-9a51-4b50-a62c-f5417e2528e9_negatedLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net distributions to noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:to="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_c90a9673-55b2-4340-a85d-b3fa3fa2eb8d_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_981bc198-d5b5-471e-a1ab-ca01b432d327_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AreaOfRealEstateProperty_3d6df221-b4c1-4268-926a-e1e8bd9218c2_terseLabel_en-US" xlink:label="lab_us-gaap_AreaOfRealEstateProperty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Area of real estate property</link:label>
    <link:label id="lab_us-gaap_AreaOfRealEstateProperty_2a905864-1f54-46c9-8d04-c141c6932a32_verboseLabel_en-US" xlink:label="lab_us-gaap_AreaOfRealEstateProperty" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Size (square feet)</link:label>
    <link:label id="lab_us-gaap_AreaOfRealEstateProperty_label_en-US" xlink:label="lab_us-gaap_AreaOfRealEstateProperty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Area of Real Estate Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AreaOfRealEstateProperty" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AreaOfRealEstateProperty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AreaOfRealEstateProperty" xlink:to="lab_us-gaap_AreaOfRealEstateProperty" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardAgreementsSettledNetProceeds_31ffb500-1840-4a96-afa2-5f153e1bc085_terseLabel_en-US" xlink:label="lab_egp_ForwardAgreementsSettledNetProceeds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward sale agreements settled, net proceeds</link:label>
    <link:label id="lab_egp_ForwardAgreementsSettledNetProceeds_label_en-US" xlink:label="lab_egp_ForwardAgreementsSettledNetProceeds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward agreements settled, net proceeds</link:label>
    <link:label id="lab_egp_ForwardAgreementsSettledNetProceeds_documentation_en-US" xlink:label="lab_egp_ForwardAgreementsSettledNetProceeds" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward agreements settled, net proceeds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardAgreementsSettledNetProceeds" xlink:href="egp-20240630.xsd#egp_ForwardAgreementsSettledNetProceeds"/>
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    <link:label id="lab_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization_f4a10cf1-4a40-44a9-93cd-60b87f578f8c_totalLabel_en-US" xlink:label="lab_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Acquired in-place lease intangibles, net of accumulated amortization</link:label>
    <link:label id="lab_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization_label_en-US" xlink:label="lab_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired In Place Lease Intangibles Net Of Accumulated Amortization</link:label>
    <link:label id="lab_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization_documentation_en-US" xlink:label="lab_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the amount of value allocated by a lessor (acquirer) to lease agreements which exist at acquisition of a leased property less accumulated amortization and any impairment charges.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization" xlink:href="egp-20240630.xsd#egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization" xlink:to="lab_egp_AcquiredInPlaceLeaseIntangiblesNetOfAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths_93122085-c742-4e59-8288-893829e401a9_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flow Hedge Gain (Loss) to be Reclassified within 12 Months</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedge Gain (Loss) to be Reclassified within 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:to="lab_us-gaap_CashFlowHedgeGainLossToBeReclassifiedWithinTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_85f074d0-0ece-490a-a213-f912cbfc7eba_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis" xlink:to="lab_us-gaap_DisposalGroupClassificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_f144c1f2-382f-4255-b879-f39a587c9eee_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_6b8fca3c-5811-4e34-b98a-ebd6f6faa123_negatedLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Common dividends declared</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_f276b922-dee9-486a-b038-0527794836c2_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_DirectCommonStockIssuancesMember_10cac3b2-d95e-4226-b280-3f4783eb73c3_terseLabel_en-US" xlink:label="lab_egp_DirectCommonStockIssuancesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct common stock issuances</link:label>
    <link:label id="lab_egp_DirectCommonStockIssuancesMember_label_en-US" xlink:label="lab_egp_DirectCommonStockIssuancesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct common stock issuances [Member]</link:label>
    <link:label id="lab_egp_DirectCommonStockIssuancesMember_documentation_en-US" xlink:label="lab_egp_DirectCommonStockIssuancesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Direct common stock issuances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_DirectCommonStockIssuancesMember" xlink:href="egp-20240630.xsd#egp_DirectCommonStockIssuancesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_DirectCommonStockIssuancesMember" xlink:to="lab_egp_DirectCommonStockIssuancesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_169c987d-e310-48ea-91c1-ba89806da89f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value [Table Text Block]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_LongtermdebtbytypeTableTextBlock_ffe9e4b5-4b05-4d5a-b58b-6e68d6b0793e_terseLabel_en-US" xlink:label="lab_egp_LongtermdebtbytypeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long term debt, by type [Table Text Block]</link:label>
    <link:label id="lab_egp_LongtermdebtbytypeTableTextBlock_label_en-US" xlink:label="lab_egp_LongtermdebtbytypeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long term debt, by type [Table Text Block]</link:label>
    <link:label id="lab_egp_LongtermdebtbytypeTableTextBlock_documentation_en-US" xlink:label="lab_egp_LongtermdebtbytypeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long term debt, by type [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_LongtermdebtbytypeTableTextBlock" xlink:href="egp-20240630.xsd#egp_LongtermdebtbytypeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_LongtermdebtbytypeTableTextBlock" xlink:to="lab_egp_LongtermdebtbytypeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOperatingIncome_4ba252a5-a47a-4ca1-86d9-cfa0a50d68c1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other revenue</link:label>
    <link:label id="lab_us-gaap_OtherOperatingIncome_label_en-US" xlink:label="lab_us-gaap_OtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherOperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOperatingIncome" xlink:to="lab_us-gaap_OtherOperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_ebc04d0d-8c72-4949-a1ef-580746486100_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_7a397679-e422-4a9f-8c3b-46d4dddec808_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized debt issuance costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredFinanceCostsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsGross" xlink:to="lab_us-gaap_DeferredFinanceCostsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_7ef19944-20cc-4384-9545-0c9412d45a50_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_f2525234-f07b-48bf-85d7-6ea1994dc702_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net Income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_d4f5d76f-b50c-4798-a37a-79680f35896d_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_624ba866-42c1-47f8-b1c0-dfabf10564e6_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">NET CASH PROVIDED BY FINANCING ACTIVITIES</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_2e379897-3c79-4590-af52-b63c2ac03d8a_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in other assets and other liabilities</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_c7d76691-d58a-488b-8a50-4264975032b5_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">TOTAL LIABILITIES AND EQUITY</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_RightofuseassetsOfficeLeases_4b2f38a9-aaa5-4f59-baba-1a56895420b8_terseLabel_en-US" xlink:label="lab_egp_RightofuseassetsOfficeLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right of use assets - Office leases (operating)</link:label>
    <link:label id="lab_egp_RightofuseassetsOfficeLeases_label_en-US" xlink:label="lab_egp_RightofuseassetsOfficeLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right of use assets - Office Leases</link:label>
    <link:label id="lab_egp_RightofuseassetsOfficeLeases_documentation_en-US" xlink:label="lab_egp_RightofuseassetsOfficeLeases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Right of use assets - Office Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_RightofuseassetsOfficeLeases" xlink:href="egp-20240630.xsd#egp_RightofuseassetsOfficeLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_RightofuseassetsOfficeLeases" xlink:to="lab_egp_RightofuseassetsOfficeLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_839fb7f6-1047-429d-9171-3a26ac57a268_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuranceSettlementsReceivable_ffef8933-98c6-40ab-be5f-75df036bf4cd_terseLabel_en-US" xlink:label="lab_us-gaap_InsuranceSettlementsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable for insurance proceeds</link:label>
    <link:label id="lab_us-gaap_InsuranceSettlementsReceivable_label_en-US" xlink:label="lab_us-gaap_InsuranceSettlementsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Settlements Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceSettlementsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InsuranceSettlementsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InsuranceSettlementsReceivable" xlink:to="lab_us-gaap_InsuranceSettlementsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_3e83ee3b-a598-411a-9ed1-dbf5fdf75b17_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right of use assets - Ground leases (operating)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_2ca5a901-55d0-44db-bd22-55e129bdc574_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Right of use assets - ground leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_cc89cb3f-eaa5-4a99-a9a3-e69b4c059e3a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2024DevelopmentLandDispositionsMember_fa53d483-0e12-4156-8d18-ffc6a849db12_terseLabel_en-US" xlink:label="lab_egp_A2024DevelopmentLandDispositionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024 development land dispositions</link:label>
    <link:label id="lab_egp_A2024DevelopmentLandDispositionsMember_label_en-US" xlink:label="lab_egp_A2024DevelopmentLandDispositionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024 development land dispositions [Member]</link:label>
    <link:label id="lab_egp_A2024DevelopmentLandDispositionsMember_documentation_en-US" xlink:label="lab_egp_A2024DevelopmentLandDispositionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024 development land dispositions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A2024DevelopmentLandDispositionsMember" xlink:href="egp-20240630.xsd#egp_A2024DevelopmentLandDispositionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A2024DevelopmentLandDispositionsMember" xlink:to="lab_egp_A2024DevelopmentLandDispositionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_7173690a-8f19-4305-adbc-6878726067b0_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_c75267d1-ed3a-4dc1-958d-14a55d7e6b08_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income Attributable to Common Stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_36cd54f7-eabe-4d2b-9431-66601452aa8a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice_d0c9c042-de36-4fff-bdb3-2a8e00dfbd21_terseLabel_en-US" xlink:label="lab_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At-the-market program, maximum aggregate gross sales price</link:label>
    <link:label id="lab_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice_label_en-US" xlink:label="lab_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At-the-market program, maximum aggregate gross sales price</link:label>
    <link:label id="lab_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice_documentation_en-US" xlink:label="lab_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At-the-market program, maximum aggregate gross sales price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice" xlink:href="egp-20240630.xsd#egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice" xlink:to="lab_egp_AtTheMarketProgramMaximumAggregateGrossSalesPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_EttieBusinessCenterMember_a86fbe5f-fa27-4cc4-a5ce-0c59e2f5d03b_terseLabel_en-US" xlink:label="lab_egp_EttieBusinessCenterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ettie Business Center</link:label>
    <link:label id="lab_egp_EttieBusinessCenterMember_label_en-US" xlink:label="lab_egp_EttieBusinessCenterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ettie Business Center [Member]</link:label>
    <link:label id="lab_egp_EttieBusinessCenterMember_documentation_en-US" xlink:label="lab_egp_EttieBusinessCenterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ettie Business Center</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_EttieBusinessCenterMember" xlink:href="egp-20240630.xsd#egp_EttieBusinessCenterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_EttieBusinessCenterMember" xlink:to="lab_egp_EttieBusinessCenterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_42c17c7a-ccfe-4c4e-a997-7ee7a2110663_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_Lineofcreditfacilityfeeinbasispoints_0026af1f-3912-4dd6-8b6b-86455aa2da82_terseLabel_en-US" xlink:label="lab_egp_Lineofcreditfacilityfeeinbasispoints" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit, facility fee (in basis points)</link:label>
    <link:label id="lab_egp_Lineofcreditfacilityfeeinbasispoints_label_en-US" xlink:label="lab_egp_Lineofcreditfacilityfeeinbasispoints" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of credit, facility fee (in basis points)</link:label>
    <link:label id="lab_egp_Lineofcreditfacilityfeeinbasispoints_documentation_en-US" xlink:label="lab_egp_Lineofcreditfacilityfeeinbasispoints" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of credit, facility fee (in basis points)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_Lineofcreditfacilityfeeinbasispoints" xlink:href="egp-20240630.xsd#egp_Lineofcreditfacilityfeeinbasispoints"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_Lineofcreditfacilityfeeinbasispoints" xlink:to="lab_egp_Lineofcreditfacilityfeeinbasispoints" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_8a22da8f-9420-4612-a853-020ee650c8a8_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_7d0317bd-adc9-43a4-ae3d-253da7ebc0c4_totalLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Real estate, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_c2f4b268-d07c-408a-bdbb-bdd81eda85d9_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RealEstateInvestmentPropertyNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebtMember_414f2153-be47-4a7f-890a-60f1c693e4fb_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Debt [Member]</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UnsecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebtMember" xlink:to="lab_us-gaap_UnsecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_GrossProceedsFromIssuanceOfCommonStock_6e0081a7-f487-4dcc-b9ad-9a8df4ca94ed_terseLabel_en-US" xlink:label="lab_egp_GrossProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Proceeds from Issuance of Common Stock</link:label>
    <link:label id="lab_egp_GrossProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_egp_GrossProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Proceeds from Issuance of Common Stock</link:label>
    <link:label id="lab_egp_GrossProceedsFromIssuanceOfCommonStock_documentation_en-US" xlink:label="lab_egp_GrossProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gross Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_GrossProceedsFromIssuanceOfCommonStock" xlink:href="egp-20240630.xsd#egp_GrossProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_GrossProceedsFromIssuanceOfCommonStock" xlink:to="lab_egp_GrossProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_2576a95f-16ef-4b25-8d62-ee0e89f03b8c_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, authorized</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_5dc9942f-583f-47f8-81b2-b0f54d334811_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments on unsecured bank credit facilities</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RepaymentsOfLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:to="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_LineOfCreditFacilityAccordion_8e6c4290-7aed-43fc-b62a-e82c26531e7d_terseLabel_en-US" xlink:label="lab_egp_LineOfCreditFacilityAccordion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit facility, accordion</link:label>
    <link:label id="lab_egp_LineOfCreditFacilityAccordion_label_en-US" xlink:label="lab_egp_LineOfCreditFacilityAccordion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of credit facility, accordion</link:label>
    <link:label id="lab_egp_LineOfCreditFacilityAccordion_documentation_en-US" xlink:label="lab_egp_LineOfCreditFacilityAccordion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of credit facility, accordion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_LineOfCreditFacilityAccordion" xlink:href="egp-20240630.xsd#egp_LineOfCreditFacilityAccordion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_LineOfCreditFacilityAccordion" xlink:to="lab_egp_LineOfCreditFacilityAccordion" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_DevelopmentAbstract_b40a450d-f9c0-400f-984b-f627da7c305a_terseLabel_en-US" xlink:label="lab_egp_DevelopmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DEVELOPMENT [Abstract]</link:label>
    <link:label id="lab_egp_DevelopmentAbstract_label_en-US" xlink:label="lab_egp_DevelopmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DEVELOPMENT [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_DevelopmentAbstract" xlink:href="egp-20240630.xsd#egp_DevelopmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_DevelopmentAbstract" xlink:to="lab_egp_DevelopmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongLivedAssetsHeldForSaleLineItems_661eda43-5231-4194-a613-1e9ba5c4d8f0_terseLabel_en-US" xlink:label="lab_us-gaap_LongLivedAssetsHeldForSaleLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Properties Sold and Held for Sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_LongLivedAssetsHeldForSaleLineItems_label_en-US" xlink:label="lab_us-gaap_LongLivedAssetsHeldForSaleLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Assets Held-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongLivedAssetsHeldForSaleLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongLivedAssetsHeldForSaleLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongLivedAssetsHeldForSaleLineItems" xlink:to="lab_us-gaap_LongLivedAssetsHeldForSaleLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsLeasingGross_9ffad282-e694-4620-aefc-a8a39879b8ce_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing costs (principally commissions)</link:label>
    <link:label id="lab_us-gaap_DeferredCostsLeasingGross_label_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Leasing, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsLeasingGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredCostsLeasingGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsLeasingGross" xlink:to="lab_us-gaap_DeferredCostsLeasingGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesDisclosureAbstract_ec7635f9-6fcb-4ff6-9fab-99a68ee8e513_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:to="lab_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_bda956d2-cc5e-4b8b-86f6-f379740d9e73_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_6b59657c-766d-47b4-a17b-8d8ad9a5a9e5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, gross</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_fe2087f3-1c44-4d48-8d93-16e411c3fd0b_totalLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, total</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_16067722-c7e8-44bd-8912-0c1941723898_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecurityDepositLiability_91897793-deea-4717-b58c-8c12ef5bcc8e_terseLabel_en-US" xlink:label="lab_us-gaap_SecurityDepositLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security deposits</link:label>
    <link:label id="lab_us-gaap_SecurityDepositLiability_label_en-US" xlink:label="lab_us-gaap_SecurityDepositLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Deposit Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecurityDepositLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SecurityDepositLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecurityDepositLiability" xlink:to="lab_us-gaap_SecurityDepositLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AwardRecipientTypeDirectorMember_c84408db-f8f4-45fc-82c6-005b1fe9d099_terseLabel_en-US" xlink:label="lab_egp_AwardRecipientTypeDirectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Recipient Type Director [Member]</link:label>
    <link:label id="lab_egp_AwardRecipientTypeDirectorMember_label_en-US" xlink:label="lab_egp_AwardRecipientTypeDirectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Recipient Type Director [Member]</link:label>
    <link:label id="lab_egp_AwardRecipientTypeDirectorMember_documentation_en-US" xlink:label="lab_egp_AwardRecipientTypeDirectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Award Recipient Type Director [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AwardRecipientTypeDirectorMember" xlink:href="egp-20240630.xsd#egp_AwardRecipientTypeDirectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AwardRecipientTypeDirectorMember" xlink:to="lab_egp_AwardRecipientTypeDirectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_08800da7-4855-4309-ae12-1c103d8019d5_verboseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gains on sales of real estate investments</link:label>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_label_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:to="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_6c380584-ab50-406c-830f-4aa1a4c422fd_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_f96e5dd6-2291-4d99-a815-98a84984f547_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EscrowDeposit_49a2c38c-bfd2-49e0-994d-e6b2e02c54d6_terseLabel_en-US" xlink:label="lab_us-gaap_EscrowDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Escrow deposits and prepaid costs for pending transactions</link:label>
    <link:label id="lab_us-gaap_EscrowDeposit_label_en-US" xlink:label="lab_us-gaap_EscrowDeposit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Escrow Deposit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EscrowDeposit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EscrowDeposit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EscrowDeposit" xlink:to="lab_us-gaap_EscrowDeposit" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ExecutiveOfficerMember_3a35febb-a956-40d9-aa00-d5c50196bcf0_terseLabel_en-US" xlink:label="lab_srt_ExecutiveOfficerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Officer [Member]</link:label>
    <link:label id="lab_srt_ExecutiveOfficerMember_label_en-US" xlink:label="lab_srt_ExecutiveOfficerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Officer [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ExecutiveOfficerMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ExecutiveOfficerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ExecutiveOfficerMember" xlink:to="lab_srt_ExecutiveOfficerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_CommonStockInSharesMember_bd0fb39b-4c17-4676-a0c9-b90b7bba4ee4_terseLabel_en-US" xlink:label="lab_egp_CommonStockInSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, in shares</link:label>
    <link:label id="lab_egp_CommonStockInSharesMember_label_en-US" xlink:label="lab_egp_CommonStockInSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common stock, in shares [Member]</link:label>
    <link:label id="lab_egp_CommonStockInSharesMember_documentation_en-US" xlink:label="lab_egp_CommonStockInSharesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common stock, in shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_CommonStockInSharesMember" xlink:href="egp-20240630.xsd#egp_CommonStockInSharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_CommonStockInSharesMember" xlink:to="lab_egp_CommonStockInSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A100millioninterestrateswap2020Member_1fe49977-d1c6-4829-b899-b9ae1f1669a4_terseLabel_en-US" xlink:label="lab_egp_A100millioninterestrateswap2020Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap (2020) [Member]</link:label>
    <link:label id="lab_egp_A100millioninterestrateswap2020Member_label_en-US" xlink:label="lab_egp_A100millioninterestrateswap2020Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap (2020) [Member]</link:label>
    <link:label id="lab_egp_A100millioninterestrateswap2020Member_documentation_en-US" xlink:label="lab_egp_A100millioninterestrateswap2020Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">$100 million interest rate swap (2020) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A100millioninterestrateswap2020Member" xlink:href="egp-20240630.xsd#egp_A100millioninterestrateswap2020Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A100millioninterestrateswap2020Member" xlink:to="lab_egp_A100millioninterestrateswap2020Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_4a5ec845-cba7-44c3-8428-7fead41cab86_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember_c12abe38-1040-4a31-8a2c-ff9aadcf013f_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases, Acquired-in-Place, Market Adjustment</link:label>
    <link:label id="lab_us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases, Acquired-in-Place, Market Adjustment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember" xlink:to="lab_us-gaap_LeasesAcquiredInPlaceMarketAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum_e0987d57-310f-4f15-8ba7-5581fff06345_terseLabel_en-US" xlink:label="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other Than Options, Potential Grants in Future Period (maximum)</link:label>
    <link:label id="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum_label_en-US" xlink:label="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other Than Options, Potential Grants in Future Period (maximum)</link:label>
    <link:label id="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum_documentation_en-US" xlink:label="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The maximum number of shares to be granted in a future period on other than stock option plans.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum" xlink:href="egp-20240630.xsd#egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum" xlink:to="lab_egp_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsPotentialGrantsInFuturePeriodMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_ff046cee-2c75-45d0-8828-6ee9a87ec147_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_d9f694d2-d5ee-4497-826c-046f163164cf_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Properties</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Properties [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_ec44efe4-b8b6-4095-ac33-fbfab22099aa_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_7e94cc77-db5a-4a1a-ba05-bfa235f9b889_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain on sales of real estate investments</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnSaleOfProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfProperties" xlink:to="lab_us-gaap_GainLossOnSaleOfProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_BlueDiamondBusinessParkMember_604a54b7-0662-4e17-9698-3ff4ea1bc61d_terseLabel_en-US" xlink:label="lab_egp_BlueDiamondBusinessParkMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Blue Diamond Business Park</link:label>
    <link:label id="lab_egp_BlueDiamondBusinessParkMember_label_en-US" xlink:label="lab_egp_BlueDiamondBusinessParkMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Blue Diamond Business Park [Member]</link:label>
    <link:label id="lab_egp_BlueDiamondBusinessParkMember_documentation_en-US" xlink:label="lab_egp_BlueDiamondBusinessParkMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Blue Diamond Business Park</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_BlueDiamondBusinessParkMember" xlink:href="egp-20240630.xsd#egp_BlueDiamondBusinessParkMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_BlueDiamondBusinessParkMember" xlink:to="lab_egp_BlueDiamondBusinessParkMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_c060f9c2-23cb-4b1b-932c-946a953671d6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_0e572a44-31f8-42f1-9563-b63516de9d08_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Other Assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost_bf29886e-2ddc-4f90-84a3-9b4cc9db6aaf_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Consideration Transferred, Transaction Cost</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Consideration Transferred, Transaction Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xlink:to="lab_us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_19c092eb-9f28-4457-90d5-b78cb2070ca2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_FairValueOfSharesVestedAsOfVestingDate_d9a72c74-b7f8-48b3-b650-29fd658fa699_terseLabel_en-US" xlink:label="lab_egp_FairValueOfSharesVestedAsOfVestingDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of shares vested as of the vesting date</link:label>
    <link:label id="lab_egp_FairValueOfSharesVestedAsOfVestingDate_label_en-US" xlink:label="lab_egp_FairValueOfSharesVestedAsOfVestingDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair value of shares vested as of the vesting date</link:label>
    <link:label id="lab_egp_FairValueOfSharesVestedAsOfVestingDate_documentation_en-US" xlink:label="lab_egp_FairValueOfSharesVestedAsOfVestingDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The vesting-date fair value of options granted during the reporting period as calculated by applying the disclosed option pricing methodology.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_FairValueOfSharesVestedAsOfVestingDate" xlink:href="egp-20240630.xsd#egp_FairValueOfSharesVestedAsOfVestingDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_FairValueOfSharesVestedAsOfVestingDate" xlink:to="lab_egp_FairValueOfSharesVestedAsOfVestingDate" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_e7df6bfb-98f6-4258-a31a-8b0c04f7e890_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncome_1839fa94-0b67-4f7c-891d-6ca419600afb_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncome_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherNonoperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncome" xlink:to="lab_us-gaap_OtherNonoperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ParkAtMyattMember_085a34c2-26bd-4de9-a195-6b5c139fec8f_terseLabel_en-US" xlink:label="lab_egp_ParkAtMyattMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Park at Myatt</link:label>
    <link:label id="lab_egp_ParkAtMyattMember_label_en-US" xlink:label="lab_egp_ParkAtMyattMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Park at Myatt [Member]</link:label>
    <link:label id="lab_egp_ParkAtMyattMember_documentation_en-US" xlink:label="lab_egp_ParkAtMyattMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Park at Myatt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ParkAtMyattMember" xlink:href="egp-20240630.xsd#egp_ParkAtMyattMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ParkAtMyattMember" xlink:to="lab_egp_ParkAtMyattMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_48f660a3-f276-479f-9bbd-7d697c2229fc_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest in joint ventures</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_72efd963-0c62-443a-bf67-be0e6f903528_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_InterestRateSwapIdentifierDomain_2740fc5a-81d2-4d8c-9647-94cf9efacc1b_terseLabel_en-US" xlink:label="lab_egp_InterestRateSwapIdentifierDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap Identifier [Domain]</link:label>
    <link:label id="lab_egp_InterestRateSwapIdentifierDomain_label_en-US" xlink:label="lab_egp_InterestRateSwapIdentifierDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap Identifier [Domain]</link:label>
    <link:label id="lab_egp_InterestRateSwapIdentifierDomain_documentation_en-US" xlink:label="lab_egp_InterestRateSwapIdentifierDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Interest Rate Swap Identifier [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_InterestRateSwapIdentifierDomain" xlink:href="egp-20240630.xsd#egp_InterestRateSwapIdentifierDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_InterestRateSwapIdentifierDomain" xlink:to="lab_egp_InterestRateSwapIdentifierDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_EachOfTheFollowingTwoYearsMember_eeacbf91-33b6-4907-8cfc-377e1bd4608b_terseLabel_en-US" xlink:label="lab_egp_EachOfTheFollowingTwoYearsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Each of the following two years</link:label>
    <link:label id="lab_egp_EachOfTheFollowingTwoYearsMember_label_en-US" xlink:label="lab_egp_EachOfTheFollowingTwoYearsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Each of the following two years [Member]</link:label>
    <link:label id="lab_egp_EachOfTheFollowingTwoYearsMember_documentation_en-US" xlink:label="lab_egp_EachOfTheFollowingTwoYearsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Each of the following two years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_EachOfTheFollowingTwoYearsMember" xlink:href="egp-20240630.xsd#egp_EachOfTheFollowingTwoYearsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_EachOfTheFollowingTwoYearsMember" xlink:to="lab_egp_EachOfTheFollowingTwoYearsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_1bc8d73e-c79e-4276-920a-0b87ddfdfd55_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding_55c08afa-ee11-46f1-9626-42a6efb99c95_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured bank credit facilities - variable rate</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Fair Value of Amount Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding" xlink:to="lab_us-gaap_LineOfCreditFacilityFairValueOfAmountOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskDisclosureTextBlock_4f3a762b-e1bb-4a17-902f-7a9cf5a3b865_verboseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ConcentrationRiskDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:to="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsLeasingAccumulatedAmortization_646e168a-fc43-4a9d-bb17-2efbc790e4a2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization of leasing costs</link:label>
    <link:label id="lab_us-gaap_DeferredCostsLeasingAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Leasing, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsLeasingAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredCostsLeasingAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsLeasingAccumulatedAmortization" xlink:to="lab_us-gaap_DeferredCostsLeasingAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_1e99745b-42c1-4fee-9632-e9c488bce0f7_verboseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_ae0a4c3d-3610-493a-83d4-1507f460f2ff_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Payment Arrangement, Expense</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetOffMarketLeaseFavorableGross_902ba591-0469-470b-b50c-09a8db339107_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetOffMarketLeaseFavorableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Above market lease intangibles</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetOffMarketLeaseFavorableGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetOffMarketLeaseFavorableGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, off-Market Lease, Favorable, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetOffMarketLeaseFavorableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetOffMarketLeaseFavorableGross"/>
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    <link:label id="lab_us-gaap_AssetAcquisitionAbstract_ba799f01-6c5a-45ac-a8ab-a6391e1adfef_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Abstract]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionAbstract"/>
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    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingShares_c67c16d7-a7a2-4fe4-8cba-5971fab33435_terseLabel_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingShares_label_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, shares</link:label>
    <link:label id="lab_egp_ForwardSaleAgreementsOutstandingShares_documentation_en-US" xlink:label="lab_egp_ForwardSaleAgreementsOutstandingShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Sale Agreements Outstanding, shares</link:label>
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    <link:label id="lab_us-gaap_AociCashFlowHedgeReferenceRateReformIncreaseDecreaseAfterTax_c9ab7245-8b60-4006-999d-0f6ec7454ef6_terseLabel_en-US" xlink:label="lab_us-gaap_AociCashFlowHedgeReferenceRateReformIncreaseDecreaseAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized change in fair value of interest rate swaps</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AociCashFlowHedgeReferenceRateReformIncreaseDecreaseAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AociCashFlowHedgeReferenceRateReformIncreaseDecreaseAfterTax"/>
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    <link:label id="lab_us-gaap_VestingAxis_b98c9c74-59ff-4c9d-91d0-276b81273ae5_terseLabel_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:label id="lab_us-gaap_VestingAxis_label_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VestingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingAxis" xlink:to="lab_us-gaap_VestingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_e677a010-2aa1-455c-8fef-9a44244b1eb2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock, common stock offering, net of expenses</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
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    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_89656fb8-55bc-4661-8c0f-01a04197b769_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average remaining lease term of acquired properties</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_CommonStockOfferingPolicyTextBlock_29f32f78-1996-4bc7-b8b9-ebcd937fd901_terseLabel_en-US" xlink:label="lab_egp_CommonStockOfferingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Offering</link:label>
    <link:label id="lab_egp_CommonStockOfferingPolicyTextBlock_label_en-US" xlink:label="lab_egp_CommonStockOfferingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Offering [Policy Text Block]</link:label>
    <link:label id="lab_egp_CommonStockOfferingPolicyTextBlock_documentation_en-US" xlink:label="lab_egp_CommonStockOfferingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Offering</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_CommonStockOfferingPolicyTextBlock" xlink:href="egp-20240630.xsd#egp_CommonStockOfferingPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_RisksAndUncertaintiesAbstract_befc5c77-dfe2-4c4e-a725-c5ff047120d3_terseLabel_en-US" xlink:label="lab_us-gaap_RisksAndUncertaintiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties [Abstract]</link:label>
    <link:label id="lab_us-gaap_RisksAndUncertaintiesAbstract_label_en-US" xlink:label="lab_us-gaap_RisksAndUncertaintiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RisksAndUncertaintiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RisksAndUncertaintiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RisksAndUncertaintiesAbstract" xlink:to="lab_us-gaap_RisksAndUncertaintiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCovenantDescription_628eee08-e1b9-433d-9da9-0f6960de0710_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCovenantDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Description</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCovenantDescription_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCovenantDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Description</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCovenantDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentCovenantDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCovenantDescription" xlink:to="lab_us-gaap_DebtInstrumentCovenantDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_339207d3-a4a5-4243-9ed0-c8ed25c82820_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_1d304d18-42db-4996-9758-c00005bb6f51_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AmendmentFlag"/>
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    <link:label id="lab_egp_InterestRateSwapIdentifierAxis_a3870282-4de7-46df-aa16-142e6c58c5df_terseLabel_en-US" xlink:label="lab_egp_InterestRateSwapIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap Identifier [Axis]</link:label>
    <link:label id="lab_egp_InterestRateSwapIdentifierAxis_label_en-US" xlink:label="lab_egp_InterestRateSwapIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap Identifier [Axis]</link:label>
    <link:label id="lab_egp_InterestRateSwapIdentifierAxis_documentation_en-US" xlink:label="lab_egp_InterestRateSwapIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap Identifier [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_InterestRateSwapIdentifierAxis" xlink:href="egp-20240630.xsd#egp_InterestRateSwapIdentifierAxis"/>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectAbstract_5eaf3144-891e-40c0-93d7-dd560bea4193_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectAbstract_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_c128e7a3-8643-4671-ba14-e31371f3308c_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, at Carrying Value</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_bf207b33-3cb2-475e-a3ac-da2fd1dcc4a4_terseLabel_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares withheld for tax obligations</link:label>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Shares Withheld for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_be9478b1-431a-417f-9c90-ca90375e401a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for interest, net of amounts capitalized of $9,890 and $7,613 for 2024 and 2023, respectively</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_8c2d4524-efbc-4d7a-ae83-0633f93fe85b_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_EndOfThreeYearPerformancePeriodMember_4ae4ad7e-2c02-4405-9fa1-88ac3ade9a04_terseLabel_en-US" xlink:label="lab_egp_EndOfThreeYearPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">End of three-year performance period</link:label>
    <link:label id="lab_egp_EndOfThreeYearPerformancePeriodMember_label_en-US" xlink:label="lab_egp_EndOfThreeYearPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">End of three-year performance period [Member]</link:label>
    <link:label id="lab_egp_EndOfThreeYearPerformancePeriodMember_documentation_en-US" xlink:label="lab_egp_EndOfThreeYearPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">End of three-year performance period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_EndOfThreeYearPerformancePeriodMember" xlink:href="egp-20240630.xsd#egp_EndOfThreeYearPerformancePeriodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_EndOfThreeYearPerformancePeriodMember" xlink:to="lab_egp_EndOfThreeYearPerformancePeriodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_85bfaf01-98a0-4df4-8b28-b2bb5fa2cbdf_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireCommercialRealEstate_bbfa0c8c-6aeb-4e2f-92b8-bd98febf9fc5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireCommercialRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of real estate</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireCommercialRealEstate_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireCommercialRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Commercial Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireCommercialRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireCommercialRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireCommercialRealEstate" xlink:to="lab_us-gaap_PaymentsToAcquireCommercialRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_b1044ed1-0505-40de-931d-cf282548f78a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from unsecured debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfUnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_c4302839-53fc-4350-b4e1-2fb11ac8998e_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_69f0f7b0-74ef-48c4-b43e-87fd082a79c6_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average diluted shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssets_ef58acf5-03ad-456d-bb92-b65ac4b669e6_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accrued income and other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases_15a16022-80e7-4d96-af6e-989a4914857f_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of above and below market leases</link:label>
    <link:label id="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases_label_en-US" xlink:label="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of above and below Market Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AmortizationOfAboveAndBelowMarketLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:to="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ShareBasedPaymentAwardstypeAxis_50b6002c-23eb-4fa9-8fd1-2f2b2501d8d6_terseLabel_en-US" xlink:label="lab_egp_ShareBasedPaymentAwardstypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Based Payment AwardsType [Axis]</link:label>
    <link:label id="lab_egp_ShareBasedPaymentAwardstypeAxis_label_en-US" xlink:label="lab_egp_ShareBasedPaymentAwardstypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Based Payment AwardsType [Axis]</link:label>
    <link:label id="lab_egp_ShareBasedPaymentAwardstypeAxis_documentation_en-US" xlink:label="lab_egp_ShareBasedPaymentAwardstypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pertinent data describing and reflecting required goals pertaining to an equity-based compensation arrangement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ShareBasedPaymentAwardstypeAxis" xlink:href="egp-20240630.xsd#egp_ShareBasedPaymentAwardstypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ShareBasedPaymentAwardstypeAxis" xlink:to="lab_egp_ShareBasedPaymentAwardstypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_d7c75fb5-1074-4dad-9e82-279f2850d108_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:to="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_409e36a5-6641-49b7-aa78-5276de71aebb_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OTHER INCOME (EXPENSE)</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseVariableLeaseIncome_1fe6eb79-178d-4d70-99d6-9f5663d54fbb_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseVariableLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable lease income</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseVariableLeaseIncome_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseVariableLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Variable Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseVariableLeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseVariableLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseVariableLeaseIncome" xlink:to="lab_us-gaap_OperatingLeaseVariableLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_e1d2e26b-804b-4527-801f-145ce7f8f6d4_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapitalCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:to="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_RealEstatePropertiesAcquiredTableTextBlock_4e9f7b05-6190-4500-892a-17f754d9a87f_terseLabel_en-US" xlink:label="lab_egp_RealEstatePropertiesAcquiredTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Properties Acquired [Table]</link:label>
    <link:label id="lab_egp_RealEstatePropertiesAcquiredTableTextBlock_label_en-US" xlink:label="lab_egp_RealEstatePropertiesAcquiredTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Properties Acquired [Table Text Block]</link:label>
    <link:label id="lab_egp_RealEstatePropertiesAcquiredTableTextBlock_documentation_en-US" xlink:label="lab_egp_RealEstatePropertiesAcquiredTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Properties Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_RealEstatePropertiesAcquiredTableTextBlock" xlink:href="egp-20240630.xsd#egp_RealEstatePropertiesAcquiredTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_RealEstatePropertiesAcquiredTableTextBlock" xlink:to="lab_egp_RealEstatePropertiesAcquiredTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_6b0da0cd-2cf4-4f4a-8353-3be6fda8f250_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_05c98332-55cf-4b01-a73d-974600316961_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured and Unsecured Debt [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfHeldToMaturitySecuritiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:to="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_4c9d2ce0-33dd-420b-80a5-334a1d45da7d_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfUnsecuredDebt_cd44fb56-6990-4419-a5c2-1921a1f369fb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments on unsecured debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfUnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfUnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RepaymentsOfUnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfUnsecuredDebt" xlink:to="lab_us-gaap_RepaymentsOfUnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_e6d3e925-98fe-4541-9b44-c77e5f74cb49_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">TOTAL ASSETS</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesMember_e7eefbb7-9d75-4e06-81b9-417c0f5f669d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities [Member]</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesMember" xlink:to="lab_us-gaap_OtherLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardEquityOfferingActivityRollForward_32ae2f52-a102-4e9e-a6cf-1340b885c57f_terseLabel_en-US" xlink:label="lab_egp_ForwardEquityOfferingActivityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward Equity Offering Activity [Roll Forward]</link:label>
    <link:label id="lab_egp_ForwardEquityOfferingActivityRollForward_label_en-US" xlink:label="lab_egp_ForwardEquityOfferingActivityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Equity Offering Activity [Roll Forward]</link:label>
    <link:label id="lab_egp_ForwardEquityOfferingActivityRollForward_documentation_en-US" xlink:label="lab_egp_ForwardEquityOfferingActivityRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Equity Offering Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardEquityOfferingActivityRollForward" xlink:href="egp-20240630.xsd#egp_ForwardEquityOfferingActivityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ForwardEquityOfferingActivityRollForward" xlink:to="lab_egp_ForwardEquityOfferingActivityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_0dee9481-5dd4-4e86-8152-1df86723977e_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_5b4d4b54-8f53-4cd9-8e3a-02e8b4ef459d_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock_b3fc0cae-1ade-4517-8a70-38fac1630cb9_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:to="lab_us-gaap_OtherLiabilitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_SpeedDistributionCenterMember_4d58f504-5228-4e89-a28d-b8ede6b5176e_terseLabel_en-US" xlink:label="lab_egp_SpeedDistributionCenterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Speed Distribution Center</link:label>
    <link:label id="lab_egp_SpeedDistributionCenterMember_label_en-US" xlink:label="lab_egp_SpeedDistributionCenterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Speed Distribution Center [Member]</link:label>
    <link:label id="lab_egp_SpeedDistributionCenterMember_documentation_en-US" xlink:label="lab_egp_SpeedDistributionCenterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Speed Distribution Center</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_SpeedDistributionCenterMember" xlink:href="egp-20240630.xsd#egp_SpeedDistributionCenterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_SpeedDistributionCenterMember" xlink:to="lab_egp_SpeedDistributionCenterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementInputsDisclosureTextBlock_45e5a350-9a5f-45d5-bcd1-c5718b7b7afe_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementInputsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementInputsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementInputsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement and Measurement Inputs, Recurring and Nonrecurring [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementInputsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementInputsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementInputsDisclosureTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementInputsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_05fe4019-8bed-4f64-ba5d-167a8e3d059f_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued in the purchase of real estate</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Purchase of Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_0ef72f9e-bcd5-4179-a08e-135085c1ef30_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested (per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles_08f2ace9-d46b-44d7-8b23-062be7a23acc_negatedTerseLabel_en-US" xlink:label="lab_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization of acquired above market lease intangibles</link:label>
    <link:label id="lab_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles_label_en-US" xlink:label="lab_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated amortization Acquired above market lease intangibles</link:label>
    <link:label id="lab_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles_documentation_en-US" xlink:label="lab_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The accumulated amount of amortization of a major finite-lived intangible asset class. A major class is composed of intangible assets that can be grouped together because they are similar, either by their nature or by their use in the operations of a company.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles" xlink:href="egp-20240630.xsd#egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles" xlink:to="lab_egp_AccumulatedAmortizationAcquiredAboveMarketLeaseIntangibles" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_3939d0d9-f616-4e88-9bb1-001dd6d26582_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Consideration Transferred</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionConsiderationTransferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:to="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2023OperatingPropertyAcquisitionsMember_27c33ae5-c4c6-45ad-aeb7-3883b0ad4848_terseLabel_en-US" xlink:label="lab_egp_A2023OperatingPropertyAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023 Operating Property Acquisitions</link:label>
    <link:label id="lab_egp_A2023OperatingPropertyAcquisitionsMember_label_en-US" xlink:label="lab_egp_A2023OperatingPropertyAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2023 Operating Property Acquisitions [Member]</link:label>
    <link:label id="lab_egp_A2023OperatingPropertyAcquisitionsMember_documentation_en-US" xlink:label="lab_egp_A2023OperatingPropertyAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2023 Operating Property Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A2023OperatingPropertyAcquisitionsMember" xlink:href="egp-20240630.xsd#egp_A2023OperatingPropertyAcquisitionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A2023OperatingPropertyAcquisitionsMember" xlink:to="lab_egp_A2023OperatingPropertyAcquisitionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_ac1c8855-190a-4475-a000-49950216cf92_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_69112a64-2931-4dd4-a15a-abf0abcf3b4e_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FINANCING ACTIVITIES</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_EndOfOneYearPerformancePeriodMember_666d1fa5-455a-4636-bb57-184f692f4137_terseLabel_en-US" xlink:label="lab_egp_EndOfOneYearPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">End of one-year performance period</link:label>
    <link:label id="lab_egp_EndOfOneYearPerformancePeriodMember_label_en-US" xlink:label="lab_egp_EndOfOneYearPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">End of one-year performance period [Member]</link:label>
    <link:label id="lab_egp_EndOfOneYearPerformancePeriodMember_documentation_en-US" xlink:label="lab_egp_EndOfOneYearPerformancePeriodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">End of one-year performance period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_EndOfOneYearPerformancePeriodMember" xlink:href="egp-20240630.xsd#egp_EndOfOneYearPerformancePeriodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_EndOfOneYearPerformancePeriodMember" xlink:to="lab_egp_EndOfOneYearPerformancePeriodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_733f6023-9dd2-4e43-a713-3f8c66bd79c9_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' Equity [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateDerivativeAssetsAtFairValue_c870792d-0075-470c-a10f-a212026f26b5_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateDerivativeAssetsAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swap assets</link:label>
    <link:label id="lab_us-gaap_InterestRateDerivativeAssetsAtFairValue_label_en-US" xlink:label="lab_us-gaap_InterestRateDerivativeAssetsAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Derivative Assets, at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateDerivativeAssetsAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestRateDerivativeAssetsAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateDerivativeAssetsAtFairValue" xlink:to="lab_us-gaap_InterestRateDerivativeAssetsAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_Arista36BusinessParkLandMember_4e6a3ee7-d5f1-4a20-a80f-586b493c0289_terseLabel_en-US" xlink:label="lab_egp_Arista36BusinessParkLandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arista 36 Business Park Land</link:label>
    <link:label id="lab_egp_Arista36BusinessParkLandMember_label_en-US" xlink:label="lab_egp_Arista36BusinessParkLandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Arista 36 Business Park Land [Member]</link:label>
    <link:label id="lab_egp_Arista36BusinessParkLandMember_documentation_en-US" xlink:label="lab_egp_Arista36BusinessParkLandMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Arista 36 Business Park Land</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_Arista36BusinessParkLandMember" xlink:href="egp-20240630.xsd#egp_Arista36BusinessParkLandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_Arista36BusinessParkLandMember" xlink:to="lab_egp_Arista36BusinessParkLandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_ff0c18a5-4166-4114-8b02-83178295219e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Debt [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_f6a42734-26fe-426f-b143-d133864068d5_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_a1e68b81-a07f-49aa-8f09-d0f0b1a5a346_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ExcessSharesParValue_1332bf42-2e2d-4cb4-b58f-2e4972297b10_terseLabel_en-US" xlink:label="lab_egp_ExcessSharesParValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess shares, par value</link:label>
    <link:label id="lab_egp_ExcessSharesParValue_label_en-US" xlink:label="lab_egp_ExcessSharesParValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Excess shares, par value</link:label>
    <link:label id="lab_egp_ExcessSharesParValue_documentation_en-US" xlink:label="lab_egp_ExcessSharesParValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Excess shares, par value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ExcessSharesParValue" xlink:href="egp-20240630.xsd#egp_ExcessSharesParValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ExcessSharesParValue" xlink:to="lab_egp_ExcessSharesParValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination_fd0409ac-88e3-4e30-897c-fd3daa3a586a_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions from noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Increase from Business Combination</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:to="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportingUnits_290d0149-3a80-474e-a856-899641205f7c_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportingUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Reporting Units</link:label>
    <link:label id="lab_us-gaap_NumberOfReportingUnits_label_en-US" xlink:label="lab_us-gaap_NumberOfReportingUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reporting Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportingUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NumberOfReportingUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportingUnits" xlink:to="lab_us-gaap_NumberOfReportingUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_A2024DevelopmentLandAcquisitionsMember_e93c91d2-7f3c-42ac-8716-94b97753594b_terseLabel_en-US" xlink:label="lab_egp_A2024DevelopmentLandAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024 development land acquisitions</link:label>
    <link:label id="lab_egp_A2024DevelopmentLandAcquisitionsMember_label_en-US" xlink:label="lab_egp_A2024DevelopmentLandAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024 development land acquisitions [Member]</link:label>
    <link:label id="lab_egp_A2024DevelopmentLandAcquisitionsMember_documentation_en-US" xlink:label="lab_egp_A2024DevelopmentLandAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024 development land acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_A2024DevelopmentLandAcquisitionsMember" xlink:href="egp-20240630.xsd#egp_A2024DevelopmentLandAcquisitionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_A2024DevelopmentLandAcquisitionsMember" xlink:to="lab_egp_A2024DevelopmentLandAcquisitionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_e346ae57-85be-4d92-ac0c-295eeefc6fe7_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">REVENUES</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization_210ffe0b-3d41-418c-8b19-8c850dfea89d_totalLabel_en-US" xlink:label="lab_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Acquired above market lease intangibles, net of accumulated amortization</link:label>
    <link:label id="lab_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization_label_en-US" xlink:label="lab_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired Above Market Leases Net Of Accumulated Amortization</link:label>
    <link:label id="lab_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization_documentation_en-US" xlink:label="lab_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the amount of value allocated by a lessor (acquirer) to lease agreements which exist at acquisition of a leased property, net of accumulated amortization. Such amount may include the value assigned to existing tenant relationships and excludes the market adjustment component of the value assigned for above .</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization" xlink:href="egp-20240630.xsd#egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization" xlink:to="lab_egp_AcquiredAboveMarketLeasesNetOfAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_SpanishRidgeIndustrialParkMember_99436132-6c5e-4067-9daf-3390234239b2_terseLabel_en-US" xlink:label="lab_egp_SpanishRidgeIndustrialParkMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Spanish Ridge Industrial Park</link:label>
    <link:label id="lab_egp_SpanishRidgeIndustrialParkMember_label_en-US" xlink:label="lab_egp_SpanishRidgeIndustrialParkMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Spanish Ridge Industrial Park [Member]</link:label>
    <link:label id="lab_egp_SpanishRidgeIndustrialParkMember_documentation_en-US" xlink:label="lab_egp_SpanishRidgeIndustrialParkMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Spanish Ridge Industrial Park</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_SpanishRidgeIndustrialParkMember" xlink:href="egp-20240630.xsd#egp_SpanishRidgeIndustrialParkMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_SpanishRidgeIndustrialParkMember" xlink:to="lab_egp_SpanishRidgeIndustrialParkMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_39222d9d-beb3-4470-8787-ef60531d3df7_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PrepaidExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForLeaseCommissions_0a9404a0-0e1a-4752-a339-31060c2d6d8c_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForLeaseCommissions" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Leasing commissions</link:label>
    <link:label id="lab_us-gaap_PaymentsForLeaseCommissions_label_en-US" xlink:label="lab_us-gaap_PaymentsForLeaseCommissions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Lease Commissions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForLeaseCommissions" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsForLeaseCommissions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForLeaseCommissions" xlink:to="lab_us-gaap_PaymentsForLeaseCommissions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_a598cd5f-1201-468a-9c12-063dd076445f_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income from real estate operations</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:to="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_9dfdd211-f014-4231-880e-1e0e35818327_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_1f7122bc-3701-4600-9f23-b3d5b433d38d_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value [Member]</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_115f915c-de4d-42a0-aba3-011b51d92a9c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCredit_38c228d8-e2de-4dc0-a9e1-754adfb12312_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unsecured bank credit facilities, net of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_ForwardEquityOfferingsAxis_60cf0e51-a62d-40d3-8eaf-515242614b46_terseLabel_en-US" xlink:label="lab_egp_ForwardEquityOfferingsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward Equity Offerings [Axis]</link:label>
    <link:label id="lab_egp_ForwardEquityOfferingsAxis_label_en-US" xlink:label="lab_egp_ForwardEquityOfferingsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Equity Offerings [Axis]</link:label>
    <link:label id="lab_egp_ForwardEquityOfferingsAxis_documentation_en-US" xlink:label="lab_egp_ForwardEquityOfferingsAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Equity Offerings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_ForwardEquityOfferingsAxis" xlink:href="egp-20240630.xsd#egp_ForwardEquityOfferingsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_ForwardEquityOfferingsAxis" xlink:to="lab_egp_ForwardEquityOfferingsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_egp_AssetsAcquiredNetOfLiabilitiesAssumed_b29d8558-7376-43bc-a366-1bbb358167a0_terseLabel_en-US" xlink:label="lab_egp_AssetsAcquiredNetOfLiabilitiesAssumed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets acquired, net of liabilities assumed</link:label>
    <link:label id="lab_egp_AssetsAcquiredNetOfLiabilitiesAssumed_label_en-US" xlink:label="lab_egp_AssetsAcquiredNetOfLiabilitiesAssumed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets acquired, net of liabilities assumed</link:label>
    <link:label id="lab_egp_AssetsAcquiredNetOfLiabilitiesAssumed_documentation_en-US" xlink:label="lab_egp_AssetsAcquiredNetOfLiabilitiesAssumed" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets acquired, net of liabilities assumed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_egp_AssetsAcquiredNetOfLiabilitiesAssumed" xlink:href="egp-20240630.xsd#egp_AssetsAcquiredNetOfLiabilitiesAssumed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_egp_AssetsAcquiredNetOfLiabilitiesAssumed" xlink:to="lab_egp_AssetsAcquiredNetOfLiabilitiesAssumed" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstatePropertiesLineItems_7281d2b5-33d3-4f34-b05a-5b5996997d71_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Properties [Line Items]</link:label>
    <link:label id="lab_us-gaap_RealEstatePropertiesLineItems_label_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Properties [Line Items]</link:label>
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