M E J Newman The structure and function of complex networks SIAM Review 45 167 256 2003文档格式.docx

M E J Newman The structure and function of complex networks SIAM Review 45 167 256 2003文档格式.docx

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Thesmall-worldmodel

27

4

A.Clusteringcoefficient

28

B.Degreedistribution

C.Averagepathlength

29

5

6 VII.

Modelsofnetworkgrowth

30

8

A.Price'

smodel

B.ThemodelofBarabasiandAlbert

31

C.GeneralizationsoftheBarabasi-Albertmodel

34

9

D.Othergrowthmodels

35

E.Vertexcopyingmodels

37

11

12VIII.

Processestakingplaceonnetworks

13

A.Percolationtheoryandnetworkresilience

38

14

B.Epidemiologicalprocesses

40

15

1.TheSIRmodel

16

2.TheSISmodel

42

17

C.Searchonnetworks

43

1.Exhaustivenetworksearch

19

2.Guidednetworksearch

44

3.Networknavigation

45

D.Phasetransitionsonnetworks

46

20

E.Otherprocessesonnetworks

47

22 IX.

Summaryanddirectionsforfutureresearch

22

23

References

48

Thestructureandfunctionofcomplexnetworks

M.E.J.Newman

DepartmentofPhysics,UniversityofMichigan,AnnArbor,Ml48109,U.S.A,and

SantaFeInstitute,1399HydeParkRoad,SantaFe,NM87501,U.S.A.

InspiredbyempiricalstudiesofnetworkedsystemssuchastheInternet,socialnetworks,andbiologicalnetworks,researchershaveinrecentyearsdevelopedavarietyoftechniquesandmodelstohelpusunderstandorpredictthebehaviorofthesesystems.Herewereviewdevelopmentsinthisfield,includingsuchconceptsasthesmall-worldeffect,degreedistributions,clustering,networkcorrelations,randomgraphmodels,modelsofnetworkgrowthandpreferentialattachment,anddynamicalprocessestakingplaceonnetworks.

Contents

Acknowledgments

I.Introduction

A.Typesofnetworks

B.Otherresources

C.Outlineofthereview

II.Networksintherealworld

A.Socialnetworks

B.Informationnetworks

C.Technologicalnetworks

D.Biologicalnetworks

III.Propertiesofnetworks

A.Thesmall-worldeffect

B.Transitivityorclustering

C.Degreedistributions

1.Scale-freenetworks

2.Maximumdegree

D.Networkresilience

E.Mixingpatterns

F.Degreecorrelations

G.Communitystructure

H.Networknavigation

I.Othernetworkproperties

IV.Randomgraphs

A.Poissonrandomgraphs

B.Generalizedrandomgraphs

1.Theconfigurationmodel

2.Example:

power-lawdegreedistribution

Forusefulfeedbackonearlyversionsofthisarticle,theauthorwouldparticularlyliketothankLadaAdamic,MichelleGirvan,PetterHolme,RandyLeVeque,SidneyRedner,RicardSole,SteveStrogatz,AlexeiVazquez,andananonymousreferee.ForotherhelpfulconversationsandcommentsaboutnetworksthanksgotoLadaAdamic,LaszloBarabasi,StefanBornholdt,DuncanCallaway,PeterDodds,JenniferDunne,RickDurrett,StephanieForrest,MichelleGirvan,JonKleinberg,JamesMoody,CrisMoore,MartinaMorris,JuyongPark,RichardRothenberg,LarryRuzzo,MatthewSalganik,LenSander,SteveStrogatz,AlessandroVespignani,ChrisWarren,DuncanWatts,andBarryWellman.Forprovidingdatausedincalculationsandfigures,thanksgotoLadaAdamic,LaszloBarabasi,JerryDavis,JenniferDunne,RamonFerreriCancho,PaulGinsparg,JerryGrossman,OlegKhovayko,HawoongJeong,DavidLipman,NeoMartinez,StephenMuth,RichardRothenberg,RicardSole,GrigoriyStarchenko,DuncanWatts,GeoffreyWest,andJanetWiener.Figure2awaskindlyprovidedbyNeoMartinezandRichardWilliamsandFig.8byJamesMoody.ThisworkwassupportedinpartbytheUSNationalScienceFoundationundergrantsDMS-0109086andDMS-0234188andbytheJamesS.McDonnellFoundationandtheSantaFeInstitute.

IIntroduction 5

I.INTRODUCTION

Anetworkisasetofitems,whichwewillcallverticesorsometimesnodes,withconnectionsbetweenthem,callededges（Fig.1）.Systemstakingtheformofnetworks（alsocalled"

graphs”inmuchofthemathematicalliterature）aboundintheworld.ExamplesincludetheInternet,theWorldWideWeb,socialnetworksofacquaintanceorotherconnectionsbetweenindividuals,organizationalnetworksandnetworksofbusinessrelationsbetweencompanies,neuralnetworks,metabolicnetworks,foodwebs,distributionnetworkssuchasbloodvesselsorpostaldeliveryroutes,networksofcitationsbetweenpapers,andmanyothers（Fig.2）.Thispaperreviewsrecent（andsomenot-so-recent）workonthestructureandfunctionofnetworkedsystemssuchasthese.

Thestudyofnetworks,intheformofmathematicalgraphtheory,isoneofthefundamentalpillarsofdiscretemathematics.Euler'

scelebrated1735solutionoftheKonigsbergbridgeproblemisoftencitedasthefirsttrueproofinthetheoryofnetworks,andduringthetwentiethcenturygraphtheoryhasdevelopedintoasubstantialbodyofknowledge.

Networkshavealsobeenstudiedextensivelyinthesocialsciences.