The shortest path to complex networks.pdf

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1、TheshortestpathtocomplexnetworksS.N.Dorogovtsev∗,†,‡andJ.F.F.Mendes∗PhysicsDepartmentoftheUniversityofAveiro,LaboratoryofPhysicsattheHelsinkiUniversityofTechnology,A.F.IoffePhysico-TechnicalInstitute,StPetersburgAbstractIntheseintroductorynotesfor‘pedestrians’wedescribethecurrent

2、stateoftheartinthescienceofcomplexnetworks.Contents1.Thebirthofnetworkscience27.Disassortativemixingdoesnotmean2.Whatarerandomnetworks?thatverticesofhighdegreesrarelycon-3.Adjacencymatrixnecttoeachother4.Degreedistribution28.Reciprocallinksindirectednetworks5.Whataresimplenetwor

3、ks?Classical29.Ultra-small-worldeffectrandomgraphs30.Theimportanceofthetreeansatz6.Thebirthofthegiantcomponent31.Ultraresilienceagainstrandomfailures7.TopologyoftheWeb32.Whencorrelatednetsareultraresilient8.Uncorrelatednetworks33.Vulnerabilityofcomplexnetworks9.Whataresmallworlds

4、?34.Theabsenceofanepidemicthreshold10.Realnetworksaremesoscopicobjects35.Searchbasedonlocalinformation11.Whatarecomplexnetworks?36.Ultraresiliencedisappearsinfinitenet-works12.Theconfigurationmodel37.Criticalbehaviorofcooperativemodels13.Theabsenceofdegree–degreecorre-onnetworksla

5、tions38.Berezinskii-Kosterlitz-Thoulessphase14.Networkswithcorrelateddegreestransitionsinnetworks15.Clustering39.Cascadingfailures16.Whataresmall-worldnetworks?40.Cliquesandcommunities17.‘Smallworlds’isnotthesameas‘small-41.Betweennessworldnetworks’42.Extractingcommunities18.Fat

6、-taileddegreedistributions43.Optimalpaths19.Reasonsforthefat-taileddegreedis-44.Distributionsoftheshortest-pathlen-tributionsgthandoftheloop’slengtharenarrow20.Preferentiallinking45.Diffusiononnetworks21.Condensationofedges46.Whatismodularity?22.Cut-offsofdegreedistributions47.Hie

7、rarchicalorganizationofnetworks23.Reasonsforcorrelationsinnetworks48.Convincingmodellingofreal-worldnet-arXiv:cond-mat/0404593v4[cond-mat.stat-mech]24Jul200424.Classicalrandomgraphscannotbeworks:Isitpossible?usedforcomparisonwithrealnetworks49.ThesmallWeb25.Howtomeasuredegree–de

8、greecorre-50.Thefailuresandperspectivesofthelat