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| function cc=clustercoeffs(A,weighted,normalized) | |
| % CLUSTERCOEFFS Compute undirected clustering coefficients for a graph | |
| % | |
| % ccfs=clustercoeffs(A) compute normalized, weighted clustering | |
| % coefficients from a graph represented by a symmetric adjacency matrix A. | |
| % | |
| % ccfs=clustering(A,weighted,normalized) takes optional parameters to | |
| % control normalization and weighted computation. If normalized=0 or | |
| % false, then the computation is not normalized by d*(d-1) in the | |
| % unweighted case. If weighted=0 or false, then the weights of the matrix | |
| % A are ignored. Either parameter will assume it's default value if you | |
| % specify an empty matrix. | |
| % | |
| % See also DIRCLUSTERCOEFFS | |
| % | |
| % Example: | |
| % load_gaimc_graph('clique-10'); | |
| % cc = clustercoeffs(A) % they are all equal! as we expect in a clique | |
| % David F. Gleich | |
| % Copyright, Stanford University, 2008-2009 | |
| % History | |
| % 2009-05-15: First history comment, originally written in 2008 | |
| if ~exist('normalized','var') || isempty(normalized), normalized=true; end | |
| if ~exist('weighted','var') || isempty(weighted), weighted=true; end | |
| donorm=1; usew=1; | |
| if ~normalized, donorm=0; end | |
| if ~weighted, usew=0; end | |
| if isstruct(A) | |
| rp=A.rp; ci=A.ci; %ofs=A.offset; | |
| if usew, ai=A.ai; end | |
| else | |
| if ~isequal(A,A'), error('gaimc:clustercoeffs',... | |
| 'only undirected (symmetric) inputs allowed: see dirclustercoeffs'); | |
| end | |
| if usew, [rp ci ai]=sparse_to_csr(A); | |
| else [rp ci]=sparse_to_csr(A); | |
| end | |
| if any(ai)<0, error('gaimc:clustercoeffs',... | |
| ['only positive edge weights allowed\n' ... | |
| 'try clustercoeffs(A,0) for an unweighted comptuation']); | |
| end | |
| end | |
| n=length(rp)-1; | |
| cc=zeros(n,1); ind=false(n,1); cache=zeros(n,1); | |
| ew=1; ew2=1; | |
| for v=1:n | |
| for rpi=rp(v):rp(v+1)-1 | |
| w=ci(rpi); if usew, ew=ai(rpi); end | |
| if v~=w, ind(w)=1; cache(w)=ew^(1/3); end | |
| end | |
| curcc=0; d=rp(v+1)-rp(v); | |
| % run two steps of bfs to try and find triangles. | |
| for rpi=rp(v):rp(v+1)-1 | |
| w=ci(rpi); if v==w, d=d-1; continue; end % discount self-loop | |
| for rpi2=rp(w):rp(w+1)-1 | |
| x=ci(rpi2); if x==w, continue; end | |
| if ind(x) | |
| if usew, ew=ai(rpi); ew2=ai(rpi2); end | |
| curcc=curcc+ew^(1/3)*ew2^(1/3)*cache(x); | |
| end | |
| end | |
| end | |
| if donorm&&d>1, cc(v)=curcc/(d*(d-1)); | |
| elseif d>1, cc(v)=curcc; | |
| end | |
| for rpi=rp(v):rp(v+1)-1, w=ci(rpi); ind(w)=0; end % reset indicator | |
| end | |