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1、PHYSICALREVIEWE74,0561082006Nonequilibriumphasetransitioninthecoevolutionofnetworksandopinions1,22PetterHolmeandM.E.J.Newman1DepartmentofComputerScience,UniversityofNewMexico,Albuquerque,NewMexico87131,USA2DepartmentofPhysics,UniversityofMichigan,AnnArbor,Michigan48109,USAReceived9March200
2、6;revisedmanuscriptreceived27September2006;published10November2006Modelsoftheconvergenceofopinioninsocialsystemshavebeenthesubjectofconsiderablerecentattentioninthephysicsliterature.Thesemodelsdivideintotwoclasses,thoseinwhichindividualsformtheirbeliefsbasedontheopinionsoftheirneighborsinaso
3、cialnetworkofpersonalacquaintances,andthoseinwhich,conversely,networkconnectionsformbetweenindividualsofsimilarbeliefs.Whilebothoftheseprocessescangiverisetorealisticlevelsofagreementbetweenacquaintances,practicalexperiencesuggeststhatopinionformationintherealworldisnotaresultofoneprocessorth
4、eother,butacombinationofthetwo.Herewepresentasimplemodelofthiscombination,withasingleparametercontrollingthebalanceofthetwoprocesses.WeÞndthatthemodelundergoesacontinuousphasetransitionasthisparameterisvaried,fromaregimeinwhichopinionsarearbitrarilydiversetooneinwhichmostindividualsholdthesam
5、eopinion.DOI:10.1103/PhysRevE.74.056108PACSnumbers:89.75.Fb,87.23.Ge,64.60.Ak,89.75.HcI.INTRODUCTIONsionofaneconomicmodelofÒpublicchoiceÓ5.ThemodelhassubstantialexperimentalsupportinbothareasSimplemathematicalmodelsdescribingemergentphe-13,14.ConsideranetworkofNvertices,representingindi
6、-nomenainhumanpopulationshavealonghistoryofstudyinviduals,joinedinpairsbyMedges,representingactiveac-thesocialsciences1.Itisonlyrelativelyrecently,however,quaintancesbetweenindividuals15.Thenumberofedgesthatphysicistshavenotedthecloseconceptualandmath-MisÞxed,reßectingthefactthatindividua
7、lscanonlymain-ematicalconnectionsbetweenthesemodelsandtraditionaltainalimitednumberofconnectionsatagivenmoment.modelsinstatisticalphysicssuchasspinmodels.BuildingThisalsoimpliesthatthenetworkissparse:theaverageonthisobservation,therehavebeena
