Subgraph centrality and clustering in complex hyper-networks.pdf

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1、ARTICLEINPRESSPhysicaA364(2006)581–594www.elsevier.com/locate/physaSubgraphcentralityandclusteringincomplexhyper-networksa,bErnestoEstrada,JuanA.Rodrı´guez-Vela´zquezaComplexSystemsResearchGroup,X-raysUnit,RIAIDT,EdificioCACTUS,UniversityofSantiagodeCo

2、mpostela,15706SantiagodeCompostela,SpainbDepartmentofMathematics,UniversityCarlosIIIdeMadrid,28911Legane´s,Madrid,SpainReceived28September2004;receivedinrevisedform1December2005Availableonline3January2006AbstractTherepresentationofcomplexsystemsasnetwo

3、rksisinappropriateforthestudyofcertainproblems.Weshowseveralexamplesofsocial,biological,ecologicalandtechnologicalsystemswheretheuseofcomplexnetworksgivesverylimitedinformationaboutthestructureofthesystem.Consequently,weextendtheconceptsofsubgraphcentr

4、alityandclusteringforcomplexnetworksrepresentedbyhypergraphs:complexhyper-networks.Thefirstparametercharacterizesthenodeparticipationindifferentsub-hypergraphsandthesecondonecharacterizesthetransitivityinthehyper-networkthroughtheproportionofhyper-trian

5、glestopathsoflengthtwo.Anothermeasurecharacterizingtheformationoftriplesofmutuallyadjacentgroupsinthehyper-networkisalsointroduced.Allofthesecharacteristicsarestudiedinthreedifferenthyper-networks:ascientificcollaborationhyper-network,anecologicalcompet

6、itionhyper-networkandthehyper-networkformedbytheAmericancorporateelitein1999.r2006ElsevierB.V.Allrightsreserved.Keywords:Centrality;Clustering;Hypergraphs;Graphspectra1.IntroductionThestudyofcomplexnetworksrepresentsanimportantareaofmultidisciplinaryre

7、searchinvolvingphysics,mathematics,chemistry,biology,socialsciences,andinformationsciences,amongothers[1–5].Thesesystemsarecommonlyrepresentedbymeanofsimpleordirectedgraphsthatconsistofsetsofnodesrepresentingtheobjectsunderinvestigation,e.g.,peopleorgr

8、oupsofpeople,molecularentities,computers,etc.,joinedtogetherinpairsbylinksifthecorrespondingnodesarerelatedbysomekindofrelationship.ThesenetworksincludetheInternet[6],theWorldWideWeb[7],socialnetworks[8–11],informationnetworks[12,13],ne