11-the structure and function of complex networks

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1、ThestructureandfunctionofcomplexnetworksM.E.J.NewmanDepartmentofPhysics,UniversityofMichigan,AnnArbor,MI48109,U.S.A.andSantaFeInstitute,1399HydeParkRoad,SantaFe,NM87501,U.S.A.InspiredbyempiricalstudiesofnetworkedsystemssuchastheInternet,socialnetworks,andbio-logicalnetworks,researc

2、hershaveinrecentyearsdevelopedavarietyoftechniquesandmodelstohelpusunderstandorpredictthebehaviorofthesesystems.Herewereviewdevelopmentsinthisfield,includingsuchconceptsasthesmall-worldeffect,degreedistributions,clustering,networkcorrelations,randomgraphmodels,modelsofnetworkgrowthan

3、dpreferentialattachment,anddynamicalprocessestakingplaceonnetworks.Contents3.Directedgraphs244.Bipartitegraphs24Acknowledgments15.Degreecorrelations25I.Introduction2V.ExponentialrandomgraphsandMarkovgraphs26A.Typesofnetworks3B.Otherresources4VI.Thesmall-worldmodel27C.Outlineofthere

4、view4A.Clusteringcoefficient28B.Degreedistribution28II.Networksintherealworld4C.Averagepathlength29A.Socialnetworks5B.Informationnetworks6VII.Modelsofnetworkgrowth30C.Technologicalnetworks8A.Price’smodel30D.Biologicalnetworks8B.ThemodelofBarab´asiandAlbert31C.GeneralizationsoftheBara

5、b´asi–Albertmodel34III.Propertiesofnetworks9D.Othergrowthmodels35A.Thesmall-worldeffect9E.Vertexcopyingmodels37B.Transitivityorclustering11C.Degreedistributions12VIII.Processestakingplaceonnetworks371.Scale-freenetworks13A.Percolationtheoryandnetworkresilience382.Maximumdegree14B.Ep

6、idemiologicalprocesses40D.Networkresilience151.TheSIRmodel40E.Mixingpatterns162.TheSISmodel42F.Degreecorrelations17C.Searchonnetworks43G.Communitystructure171.Exhaustivenetworksearch43H.Networknavigation192.Guidednetworksearch44I.Othernetworkproperties193.Networknavigation45D.Phase

7、transitionsonnetworks46IV.Randomgraphs20E.Otherprocessesonnetworks47A.Poissonrandomgraphs20B.Generalizedrandomgraphs22IX.Summaryanddirectionsforfutureresearch471.Theconfigurationmodel222.Example:power-lawdegreedistribution23References48AcknowledgmentsForusefulfeedbackonearlyversions

8、ofthisarticle,theauthorwou