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- function C=clustering_coef_wd(W)
- %CLUSTERING_COEF_WD Clustering coefficient
- %
- % C = clustering_coef_wd(W);
- %
- % The weighted clustering coefficient is the average "intensity"
- % (geometric mean) of all triangles associated with each node.
- %
- % Input: W, weighted directed connection matrix
- % (all weights must be between 0 and 1)
- %
- % Output: C, clustering coefficient vector
- %
- % Reference: Fagiolo (2007) Phys Rev E 76:026107.
- %
- % Note: All weights must be between 0 and 1.
- % This may be achieved using the weight_conversion.m function,
- % W_nrm = weight_conversion(W, 'normalize');
- %
- % Mika Rubinov, UNSW/U Cambridge, 2007-2015
- % Modification history:
- % 2007: original
- % 2015: expanded documentation
- % Methodological note (also see clustering_coef_bd)
- % The weighted modification is as follows:
- % - The numerator: adjacency matrix is replaced with weights matrix ^ 1/3
- % - The denominator: no changes from the binary version
- %
- % The above reduces to symmetric and/or binary versions of the clustering
- % coefficient for respective graphs.
- A=W~=0; %adjacency matrix
- S=W.^(1/3)+(W.').^(1/3); %symmetrized weights matrix ^1/3
- K=sum(A+A.',2); %total degree (in + out)
- cyc3=diag(S^3)/2; %number of 3-cycles (ie. directed triangles)
- K(cyc3==0)=inf; %if no 3-cycles exist, make C=0 (via K=inf)
- CYC3=K.*(K-1)-2*diag(A^2); %number of all possible 3-cycles
- C=cyc3./CYC3; %clustering coefficient
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