签订房屋租赁合同的十大注意事项

Lecture5:NetworkcentralitySlidesaremodifiedfromLadaAdamic太原房产网Knowingthestructureofanetwork,wecancalculatevarioususefulquantitiesormeasuresthatcaptureparticularfeaturesofthenetworktopology.basisofmostofsuchmeasuresarefromsocialnetworkanalysisSofar,Degreedistribution,Averagepathlength,DensityCentralityDegree,Eigenvector,Katz,PageRank,Hubs,Closeness,Betweenness,….SeveralothergraphmetricsClusteringcoefficient,Assortativity,Modularity,…2Characterizingnetworks:Whoismostcentral????3networkcentralityWhichnodesaremost‘central’?Definitionof‘central’variesbycontext/purposeLocalmeasure:degreeRelativetorestofnetwork:closeness,betweenness,eigenvector(Bonacichpowercentrality),Katz,PageRank,…Howevenlyiscentralitydistributedamongnodes?Centralization,hubsandautthorities,…4centrality:who’simportantbasedontheirnetworkpositionindegreeIneachofthefollowingnetworks,XhashighercentralitythanYaccordingtoaparticularmeasureoutdegreebetweennesscloseness5OutlineDegreecentralityCentralizationBetweennesscentralityClosenesscentralityEigenvectorcentralityBonacichpowercentralityKatzcentralityPageRankHubsandAuthorities6Hewhohasmanyfriendsismostimportant.degreecentrality(undirected)Whenisthenumberofconnectionsthebestcentralitymeasure?opeoplewhowilldofavorsforyouopeopleyoucantalkto(influenceset,informationaccess,…)oinfluenceofanarticleintermsofcitations(usingin-degree)7degree:normalizeddegreecentralitydividebythemax.possible,i.e.(N-1)8Prestigeindirectedsocialnetworkswhen‘prestige’maybetherightwordadmirationinfluencegift-givingtrustdirectionalityespeciallyimportantininstanceswheretiesmaynotbereciprocated(e.g.diningpartnerschoicenetwork)when‘prestige’maynotbetherightwordgivesadviceto(canreversedirection)givesordersto(-”-)lendsmoneyto(-”-)dislikesdistrusts9Extensionsofundirecteddegreecentrality-prestigedegreecentralityindegreecentralityapaperthatiscitedbymanyothershashighprestigeapersonnominatedbymanyothersforarewardhashighprestige10Freeman’sgeneralformulaforcentralization:(canuseothermetrics,e.g.ginicoefficientorstandarddeviation)CDCD(n*)CD(i)i1g[(N1)(N2)]centralization:howequalarethenodes?Howmuchvariationisthereinthecentralityscoresamongthenodes?maximumvalueinthenetwork11degreecentralizationexamplesCD=0.167CD=0.167CD=1.012degreecentralizationexamplesexamplefinancialtradingnetworkshighcentralization:onenodetradingwithmanyotherslowcentralization:tradesaremoreevenlydistributed13whendegreeisn’teverythingInwhatwaysdoesdegreefailtocapturecentralityinthefollowinggraphs?abilitytobrokerbetweengroupslikelihoodthatinformationoriginatinganywhereinthenetworkreachesyou…14OutlineDegreecentralityCentralizationBetweennesscentralityClosenesscentrality15betweenness:anothercentralitymeasureintuition:howmanypairsofindividualswouldhavetogothroughyouinordertoreachoneanotherintheminimumnumberofhops?whohashigherbetweenness,XorY?XY16CB(i)gjk(i)/gjkjkWheregjk=thenumberofgeodesicsconnectingj-k,andgjk=thenumberthatactoriison.Usuallynormalizedby:CB'(i)CB(i)/[(n1)(n2)/2]numberofpairsofverticesexcludingthevertexitselfbetweennesscentrality:definition17betweennessofvertexipathsbetweenjandkthatpassthroughiallpathsbetweenjandkdirectedgraph:(N-1)*(N-2)betweennessontoynetworksnon-normalizedversion:ABCEDAliesbetweennotwootherverticesBliesbetweenAand3othervertices:C,D,andECliesbetween4pairsofvertices(A,D),(A,E),(B,D),(B,E)notethattherearenoalternatepathsforthesepairstotake,soCgetsfullcredit18betweennessontoynetworksnon-normalizedversion:19betweennessontoynetworksnon-normalizedversion:20brokerNodesaresizedbydegree,andcoloredbybetweenness.exampleCanyouspotnodeswithhighbetweennessbutrelativelylowdegree?Whatabouthighdegreebutrelativelylowbetweenness?21betweennessontoynetworksnon-normalizedversion:ABCEDwhydoCandDeachhavebetweenness1?Theyarebothonshortestpathsforpairs(A,E),and(B,E),andsomustsharecredit:½+½=1CanyoufigureoutwhyBhasbetweenness3.5whileEhasbetweenness0.5?22AlternativebetweennesscomputationsSlightvariationsingeodesicpathcomputationsinclusionofselfinthecomputationsFlowbetweennessBasedontheideaofmaximumflowedge-independentpathselectioneffectstheresultsMaynotincludegeodesicpathsRandom-walkbetweennessBasedontheideaofrandomwalksUsuallyyieldsrankingsimilartogeodesicbetweennessManyotheralternativedefinitionsexistbasedondiffusion,transmissionorflowalongnetworkedges23ExtendingbetweennesscentralitytodirectednetworksWenowconsiderthefractionofalldirectedpathsbetweenanytwoverticesthatpassthroughanodeOnlymodification:whennormalizing,wehave(N-1)*(N-2)insteadof(N-1)*(N-2)/2,becausewehavetwiceasmanyorderedpairsasunorderedpairsCB(i)gjkj,k(i)/gjkbetweennessofvertexipathsbetweenjandkthatpassthroughiallpathsbetweenjandkCB'(i)CB(i)/[(N1)(N2)]24DirectedgeodesicsAnodedoesnotnecessarilylieonageodesicfromjtokifitliesonageodesicfromktojkj25OutlineDegreecentralityCentralizationBetweennesscentralityClosenesscentrality26closeness:anothercentralitymeasureWhatifit’s