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1、functionC=clustering_coef_bd(A)%C=clustering_coef_bd(A);clusteringcoefficientC,forbinarydirectedgraphA%%Reference:Fagiolo,2007,PhysRevE76:026107.%%MikaRubinov,UNSW,2007(lastmodifiedJuly2008)%Indirectedgraphs,3nodesgenerateupto8triangles(2*2*2edges)%Thenumberofexistingtriangl
2、esisthemaindiagonalofS^3/2%Thenumberofall(inorout)neighbourpairsisK(K-1)/2%Eachneighbourpairmaygeneratetwotriangles%"Falsepairs"arei<->jedgepairs(thesedonotgeneratetriangles)%ThenumberoffalsepairsisthemaindiagonalofA^2%Thusthemaximumpossiblenumberoftriangles=%=(2edges)*([ALL
3、PAIRS]-[FALSEPAIRS])=%=2*(K(K-1)/2-diag(A^2))=K(K-1)-2(diag(A^2))S=A+A.';%symmetrizedinputgraphK=sum(S,2);%totaldegree(in+out)cyc3=diag(S^3)/2;%numberof3-cycles(ie.directedtriangles)K(cyc3==0)=inf;%ifno3-cyclesexist,makeC=0(viaK=inf)CYC3=K.*(K-1)-2*diag(A^2);%numberofallposs
4、ible3-cyclesC=cyc3./CYC3;%clusteringcoefficientfunctionC=clustering_coef_bu(G)%C=clustering_coef_bu(G);clusteringcoefficientC,forbinaryundirectedgraphG%%Reference:WattsandStrogatz,1998,Nature393:440-442%%MikaRubinov,UNSW,2007(lastmodifiedSeptember2008)n=length(G);C=zeros(n,1
5、);foru=1:nV=find(G(u,:));k=length(V);ifk>=2;%degreemustbeatleast2S=G(V,V);C(u)=sum(S(:))/(k^2-k);endendfunctionC=clustering_coef_wd(W)%C=clustering_coef_wd(W);clusteringcoefficientCforweighteddirectedgraphW.%%Reference:Fagiolo,2007,PhysRevE76:026107%(alsoseeOnnelaetal.2005,P
6、hysRevE71:065103);%%MikaRubinov,UNSW,2007(lastmodifiedJuly2008)%Seecommentsforclustering_coef_bd%Theweightedmodificationisasfollows:%-Thenumerator:adjacencymatrixisreplacedwithweightsmatrix^1/3%-Thedenominator:nochangesfromthebinaryversion%%Theabovereducestosymmetricand/orbi
7、naryversionsofthe%clusteringcoefficientforrespectivegraphs.A=W~=0;%adjacencymatrixS=W.^(1/3)+(W.').^(1/3);%symmetrizedweightsmatrix^1/3K=sum(A+A.',2);%totaldegree(in+out)cyc3=diag(S^3)/2;%numberof3-cycles(ie.directedtriangles)K(cyc3==0)=inf;%ifno3-cyclesexist,makeC=0(viaK=in
8、f)CYC3=K.*(K-1)-2*diag(A^2);%numberofallpossible3-cyclesC=cyc3./CYC3;%clust
