path_transitivity.m
3209cc2b0b1dmaster

path_transitivity.m
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			function T=path_transitivity(W,transform)
			% PATH_TRANSITIVITY Transitivity based on shortest paths
			%
			% T = path_transitivity(W,transform)
			%
			% This function computes the density of local detours (triangles) that
			% are available along the shortest-paths between all pairs of nodes.
			%
			% Inputs:
			%
			% W,
			% unweighted/weighted undirected connection weight OR length
			% matrix.
			%
			%
			% transform,
			% If the input matrix is a connection weight matrix, specify a
			% transform that map input connection weights to connection
			% lengths. Two transforms are available.
			% 'log' -> l_ij = -log(w_ij)
			% 'inv' -> l_ij = 1/w_ij
			%
			% If the input matrix is a connection length matrix, do not
			% specify a transform (or specify an empty transform argument).
			%
			%
			% Output:
			%
			% T,
			% matrix of pairwise path transitivity.
			%
			%
			% Olaf Sporns, Andrea Avena-Koenigsberger and Joaquin Goñi, IU Bloomington, 2014
			%
			% References: Goñi et al (2014) PNAS doi: 10.1073/pnas.131552911
			%

			if ~exist('transform','var')
			transform = [];
			end

			n=length(W);
			m=zeros(n,n);
			T=zeros(n,n);

			for i=1:n-1
			for j=i+1:n
			x=0;
			y=0;
			z=0;
			for k=1:n
			if W(i,k)~=0 && W(j,k)~=0 && k~=i && k~=j
			x=x+W(i,k)+W(j,k);
			end
			if k~=j
			y=y+W(i,k);
			end
			if k~=i
			z=z+W(j,k);
			end
			end
			m(i,j)=x/(y+z);
			end
			end
			m=m+m';

			[~,hops,Pmat] = distance_wei_floyd(W,transform);

			% --- path transitivity ---%%
			for i=1:n-1
			for j=i+1:n
			x=0;
			path = retrieve_shortest_path(i,j,hops,Pmat);
			K=length(path);

			for t=1:K-1
			for l=t+1:K
			x=x+m(path(t),path(l));
			end
			end
			T(i,j)=2x/(K(K-1));
			end
			end
			T=T+T';