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| function [cc cccyc ccmid ccin ccout nf]=dirclustercoeffs(A,weighted,normalized) | |
| % DIRCLUSTERCOEFFS Compute clustering coefficients for a directed graph | |
| % | |
| % cc=dirclustercoeffs(A) returns the directed clustering coefficients | |
| % (which generalize the clustering coefficients of an undirected graph, | |
| % and so calling this function on an undirected graph will produce the same | |
| % answer as clustercoeffs, but less efficiently.) | |
| % | |
| % This function implements the algorithm from Fagiolo, Phys Rev. E. 76 | |
| % 026107 (doi:10:1103/PhysRevE.76.026107). | |
| % | |
| % [cc,cccyc,ccmid,ccin,ccout,nf]=dirclusteringcoeffs(A) returns different | |
| % components of the clustering coefficients corresponding to cycles, | |
| % middles, in triangles, and out triangles. See the manuscript for a | |
| % description of the various types of triangles counted in the above | |
| % metrics. | |
| % | |
| % See also CLUSTERCOEFFS | |
| % | |
| % Example: | |
| % load_gaimc_graph('celegans'); % load the C elegans nervous system network | |
| % cc=dirclustercoeffs(A); | |
| % [maxval maxind]=max(cc) | |
| % labels(maxind) % most clustered vertex in the nervous system | |
| % David F. Gleich | |
| % Copyright, Stanford University, 2008-2009 | |
| % History | |
| % 2008-04-22: Initial coding | |
| % 2009-05-15: Documentation and example | |
| 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; | |
| cp=A.cp; ri=A.ri; % get | |
| if usew, ai=A.ai; ati=A.ati; end | |
| else | |
| if usew, [rp ci ai]=sparse_to_csr(A); [cp ri ati]=sparse_to_csr(A'); | |
| else [rp ci]=sparse_to_csr(A); [cp ri]=sparse_to_csr(A'); | |
| end | |
| if any(ai)<0, error('gaimc:clustercoeffs',... | |
| ['only positive edge weights allowed\n' ... | |
| 'try dirclustercoeffs(A,0) for an unweighted comptuation']); | |
| end | |
| end | |
| n=length(rp)-1; | |
| % initialize all the variables | |
| cc=zeros(n,1); ind=false(n,1); cache=zeros(n,1); degs=zeros(n,1); | |
| if nargout>1, cccyc=zeros(n,1); end | |
| if nargout>2, ccmid=zeros(n,1); end | |
| if nargout>3, ccin=zeros(n,1); end | |
| if nargout>4, ccout=zeros(n,1); end | |
| if nargout>5, nf=zeros(n,1); end | |
| % precompute degrees | |
| for v=1:n, | |
| for rpi=rp(v):rp(v+1)-1, | |
| w=ci(rpi); | |
| if v==w, continue; else degs(w)=degs(w)+1; degs(v)=degs(v)+1; end | |
| end | |
| end | |
| ew=1; ew2=1; | |
| for v=1:n | |
| % setup counts for the different cycle types | |
| bilatedges=0; curcccyc=0; curccmid=0; curccin=0; curccout=0; | |
| % 1. | |
| % find triangles with out links as last step, so precompute the inlinks | |
| % back to node v | |
| for cpi=cp(v):cp(v+1)-1 | |
| w=ri(cpi); if usew, ew=ati(cpi); end | |
| if v~=w, ind(w)=1; cache(w)=ew^(1/3); end | |
| end | |
| % count cycles (cycles are out->out->out) | |
| for rpi=rp(v):rp(v+1)-1 | |
| w=ci(rpi); if v==w, continue; end % discount self-loop | |
| if usew, ew=ai(rpi)^(1/3); end | |
| for rpi2=rp(w):rp(w+1)-1 | |
| x=ci(rpi2); if x==w, continue; end | |
| if x==v, bilatedges=bilatedges+1; continue; end | |
| if ind(x) | |
| if usew, ew2=ai(rpi2); end | |
| curcccyc=curcccyc+ew*ew2^(1/3)*cache(x); | |
| end | |
| end | |
| end | |
| % count middle-man circuits (out->in->out) | |
| for rpi=rp(v):rp(v+1)-1 | |
| w=ci(rpi); if v==w, continue; end % discount self-loop | |
| if usew, ew=ai(rpi)^(1/3); end | |
| for cpi=cp(w):cp(w+1)-1 | |
| x=ri(cpi); if x==w, continue; end | |
| if ind(x) | |
| if usew, ew2=ati(cpi); end | |
| curccmid=curccmid+ew*ew2^(1/3)*cache(x); | |
| end | |
| end | |
| end | |
| % count in-link circuits (in->out->out) | |
| for cpi=cp(v):cp(v+1)-1 | |
| w=ri(cpi); if v==w, continue; end % discount self-loop | |
| if usew, ew=ati(cpi)^(1/3); end | |
| for rpi2=rp(w):rp(w+1)-1 | |
| x=ci(rpi2); if x==w, continue; end | |
| if ind(x) | |
| if usew, ew2=ai(rpi2); end | |
| curccin=curccin+ew*ew2^(1/3)*cache(x); | |
| end | |
| end | |
| end | |
| % reset and reinit the cache for outlinks | |
| for cpi=cp(v):cp(v+1)-1, w=ri(cpi); ind(w)=0; end % reset indicator | |
| 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 | |
| % count out-link circuits (out->out->in) | |
| for rpi=rp(v):rp(v+1)-1 | |
| w=ci(rpi); if v==w, continue; end % discount self-loop | |
| if usew, ew=ai(rpi)^(1/3); end | |
| for rpi2=rp(w):rp(w+1)-1 | |
| x=ci(rpi2); if x==w, continue; end | |
| if ind(x) | |
| if usew, ew2=ai(rpi2); end | |
| curccout=curccout+ew*ew2^(1/3)*cache(x); | |
| end | |
| end | |
| end | |
| for rpi=rp(v):rp(v+1)-1, w=ci(rpi); ind(w)=0; end % reset indicator | |
| % store the values | |
| nf=degs(v)*(degs(v)-1) - 2*bilatedges; | |
| curcc=curcccyc+curccmid+curccin+curccout; | |
| if nf>0 && donorm, curcc=curcc/nf; end | |
| cc(v)=curcc; | |
| if nargout>1, cccyc(v)=curcccyc; end | |
| if nargout>2, ccmid(v)=curccmid; end | |
| if nargout>3, ccin(v)=curccin; end | |
| if nargout>4, ccout(v)=curccout; end | |
| if nargout>5, nf(v)=nf; end | |
| end |