签订房屋租赁合同的十大注意事项

Lecture5:Networkcentrality,SlidesaremodifiedfromLadaAdamic,太原房产网,MeasuresandMetrics,Knowingthestructureofanetwork,wecancalculatevarioususefulquantitiesormeasuresthatcaptureparticularfeaturesofthenetworktopology.basisofmostofsuchmeasuresarefromsocialnetworkanalysisSofar,Degreedistribution,Averagepathlength,DensityCentralityDegree,Eigenvector,Katz,PageRank,Hubs,Closeness,Betweenness,.SeveralothergraphmetricsClusteringcoefficient,Assortativity,Modularity,2,Characterizingnetworks:Whoismostcentral?,3,networkcentrality,Whichnodesaremostcentral?Definitionofcentralvariesbycontext/purposeLocalmeasure:degreeRelativetorestofnetwork:closeness,betweenness,eigenvector(Bonacichpowercentrality),Katz,PageRank,Howevenlyiscentralitydistributedamongnodes?Centralization,hubsandautthorities,4,centrality:whosimportantbasedontheirnetworkposition,indegree,Ineachofthefollowingnetworks,XhashighercentralitythanYaccordingtoaparticularmeasure,outdegree,betweenness,closeness,5,Outline,DegreecentralityCentralizationBetweennesscentralityClosenesscentralityEigenvectorcentralityBonacichpowercentralityKatzcentralityPageRankHubsandAuthorities,6,Hewhohasmanyfriendsismostimportant.,degreecentrality(undirected),Whenisthenumberofconnectionsthebestcentralitymeasure?peoplewhowilldofavorsforyoupeopleyoucantalkto(influenceset,informationaccess,)influenceofanarticleintermsofcitations(usingin-degree),7,degree:normalizeddegreecentrality,dividebythemax.possible,i.e.(N-1),8,Prestigeindirectedsocialnetworks,whenprestigemaybetherightwordadmirationinfluencegift-givingtrustdirectionalityespeciallyimportantininstanceswheretiesmaynotbereciprocated(e.g.diningpartnerschoicenetwork)whenprestigemaynotbetherightwordgivesadviceto(canreversedirection)givesordersto(-”-)lendsmoneyto(-”-)dislikesdistrusts,9,Extensionsofundirecteddegreecentrality-prestige,degreecentralityindegreecentralityapaperthatiscitedbymanyothershashighprestigeapersonnominatedbymanyothersforarewardhashighprestige,10,Freemansgeneralformulaforcentralization:(canuseothermetrics,e.g.ginicoefficientorstandarddeviation),centralization:howequalarethenodes?,Howmuchvariationisthereinthecentralityscoresamongthenodes?,maximumvalueinthenetwork,11,degreecentralizationexamples,CD=0.167,CD=0.167,CD=1.0,12,degreecentralizationexamples,examplefinancialtradingnetworks,highcentralization:onenodetradingwithmanyothers,lowcentralization:tradesaremoreevenlydistributed,13,whendegreeisnteverything,Inwhatwaysdoesdegreefailtocapturecentralityinthefollowinggraphs?,abilitytobrokerbetweengroupslikelihoodthatinformationoriginatinganywhereinthenetworkreachesyou,14,Outline,DegreecentralityCentralizationBetweennesscentralityClosenesscentrality,15,betweenness:anothercentralitymeasure,intuition:howmanypairsofindividualswouldhavetogothroughyouinordertoreachoneanotherintheminimumnumberofhops?whohashigherbetweenness,XorY?,X,Y,16,Wheregjk=thenumberofgeodesicsconnectingj-k,andgjk=thenumberthatactoriison.,Usuallynormalizedby:,numberofpairsofverticesexcludingthevertexitself,betweennesscentrality:definition,17,betweennessofvertexi,pathsbetweenjandkthatpassthroughi,allpathsbetweenjandk,directedgraph:(N-1)*(N-2),betweennessontoynetworks,non-normalizedversion:,A,B,C,E,D,AliesbetweennotwootherverticesBliesbetweenAand3othervertices:C,D,andECliesbetween4pairsofvertices(A,D),(A,E),(B,D),(B,E)notethattherearenoalternatepathsforthesepairstotake,soCgetsfullcredit,18,betweennessontoynetworks,non-normalizedversion:,19,betweennessontoynetworks,non-normalizedversion:,20,broker,Nodesaresizedbydegree,andcoloredbybetweenness.,example,Canyouspotnodeswithhighbetweennessbutrelativelylowdegree?,Whatabouthighdegreebutrelativelylowbetweenness?,21,betweennessontoynetworks,non-normalizedversion:,A,B,C,E,D,whydoCandDeachhavebetweenness1?Theyarebothonshortestpathsforpairs(A,E),and(B,E),andsomustsharecredit:+=1CanyoufigureoutwhyBhasbetweenness3.5whileEhasbetweenness0.5?,22,Alternativebetweennesscomputations,SlightvariationsingeodesicpathcomputationsinclusionofselfinthecomputationsFlowbetweennessBasedontheideaofmaximumflowedge-independentpathselectioneffectstheresultsMaynotincludegeodesicpathsRandom-walkbetweennessBasedontheideaofrandomwalksUsuallyyieldsrankingsimilartogeodesicbetweennessManyotheralternativedefinitionsexistbasedondiffusion,transmissionorflowalongnetworkedges,23,Extendingbetweennesscentralitytodirectednetworks,Wenowconsiderthefractionofalldirectedpathsbetweenanytwoverticesthatpassthroughanode,Onlymodification:whennormalizing,wehave(N-1)*(N-2)insteadof(N-1)*(N-2)/2,becausewehavetwiceasmanyorderedpairsasunorderedpairs,betweennessofvertexi,pathsbetweenjandkthatpassthroughi,allpathsbetweenjandk,24,Directedgeodesics,Anodedoesnotnecessarilylieonageodesicfromjtokifitliesonageodesicfromktoj,k,j,25,Outline,DegreecentralityCentralizationBetweennesscentralityClosenesscentrality,26,closeness:anothercentralitymeasure,Whatifitsnotsoimportanttohavemanydirectfriends?Orbe“between”othersButonestillwantstobeinthe“middle”ofthings,nottoofarfromthecenter,27,Closenessisbasedonthelengthoftheaverageshortestpathbetweenavertexandallverticesinthegraph,ClosenessCentrality:,NormalizedClosenessCentrality,closenesscentrality:definition,28,dependsoninversedistancetoothervertices,closenesscentrality:toyexample,A,B,C,E,D,29,closenesscentrality:moretoyexamples,30,degreenumberofconnectionsdenotedbysizeclosenesslengthofshortestpathtoallothersdenotedbycolor,howcloselydodegreeandbetweennesscorrespondtocloseness?,31,Closenesscentrality,Valuestendtospanarathersmal