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1、MixturemodelsandexploratoryanalysisinnetworksM.E.J.NewmanandE.A.LeichtDepartmentofPhysics,UniversityofMichigan,AnnArbor,MI48109,USANetworksarewidelyusedinthebiological,physical,andsocialsciencesasaconcisemathematicalrepresentationofthetopologyofsystemsofinteract
2、ingcomponents.Understandingthestructureofthesenetworksisoneoftheoutstandingchallengesinthestudyofcomplexsystems.Herewedescribeageneraltechniquefordetectingstructuralfeaturesinlarge-scalenetworkdatawhichworksbydividingthenodesofanetworkintoclassessuchthatthemembe
3、rsofeachclasshavesimilarpatternsofconnectiontoothernodes.Usingthemachineryofprobabilisticmixturemodelsandtheexpectation-maximizationalgorithm,weshowthatitispossibletodetect,withoutpriorknowledgeofwhatwearelookingfor,averybroadrangeoftypesofstructureinnetworks.We
4、giveanumberofexamplesdemonstratinghowthemethodcanbeusedtoshedlightonthepropertiesofreal-worldnetworks,includingsocialandinformationnetworks.INTRODUCTIONtributionmayshowinterestingfeatures.Thisapproachhascertainlyworkedwell—manyilluminatingdiscover-Inthelastfewye
5、ars,networkshavefounduseinmanyieshavebeenmadethisway.Butitraisesanuncom-?eldsasapowerfultoolforrepresentingthestructureoffortablequestion:couldtherebeinterestingandrelevantcomplexsystems[1,2,3,4].Metabolic,proteininter-structuralfeaturesofnetworksthatwehavefaile
6、dto?ndaction,andgeneticregulatorynetworksarenowheavilysimplybecausewehaven’tthoughttomeasuretherightstudiedinbiologyandmedicine,theInternetandthething?worldwidewebincomputerandinformationsciences,Tosomeextentthisisanissuewiththewholeofscien-foodwebsandotherspeci
7、esinteractionnetworksinecol-ti?cendeavor.Inany?eldthinkingoftherightquestionogy,andnetworksofpersonalorsocialcontactsinepi-candemandasmuchinsightasthinkingoftheanswer.demiology,sociology,andthemanagementsciences.However,therearealsothingswecandotohelpour-Thestud
8、yofnetworksgoesbackmuchfurtherthanselves.Inthispaperwedescribeatechniquethatallowsthecurrentsurgeofinterestinit,butrecentworkdi?ersustodetectstructureinnetworkdatawhi
