Thispaperstudiesasimpleasymmetricallyevolvedcommunitynetworkwithacombinationofpreferentialattachmentandrandomproperties.Animportantissueaboutcommunitynetworksistodiscoverthedifferentutilityincrementsoftwonodes,wheretheutilityisintroducedtoinvestigatetheasymmetricaleffectofconnectingtwonodes.Ontheotherhand,theconnectionoftwonodesincommunitynetworkscanbeclassifiedastwonodesbelongingtothesameortodifferentcommunities.Thesimulationresultsshowthatthemodelcanreproduceapower-lawutilitydistributionP(u)～uσ,σ=2+1p,whichcanbeobtainedbyusingmean-fieldapproximationmethods.Furthermore,themodelexhibitsexponentialbehaviourwithrespecttosmallvaluesofaparameterdenotingtherandomeffectinourmodelatthelow-utilityregionandapower-lawfeaturewithrespecttobigvaluesofthisparameteratthehigh-utilityregion,whichisingoodagreementwiththeoreticalanalysis.Thiskindofcommunitynetworkcanreproduceauniqueutilitydistributionbytheoreticalandnumericalanalysis.
