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ISFCClustering/2019_03_03_BCT/assortativity_wei.m
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assortativity_wei.m
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function r = assortativity_wei(CIJ,flag)
% ASSORTATIVITY_WEI Assortativity coefficient
%
% r = assortativity_wei(CIJ,flag);
%
% The assortativity coefficient is a correlation coefficient between the
% strengths (weighted degrees) of all nodes on two opposite ends of a link.
% A positive assortativity coefficient indicates that nodes tend to link to
% other nodes with the same or similar strength.
%
% Inputs: CIJ, weighted directed/undirected connection matrix
% flag, 0, undirected graph: strength/strength correlation
% 1, directed graph: out-strength/in-strength correlation
% 2, directed graph: in-strength/out-strength correlation
% 3, directed graph: out-strength/out-strength correlation
% 4, directed graph: in-strength/in-strength correlation
%
% Outputs: r, assortativity coefficient
%
% Notes: The main diagonal should be empty. For flag 1 the function computes
% the directed assortativity described in Rubinov and Sporns (2010) NeuroImage.
%
% Reference: Newman (2002) Phys Rev Lett 89:208701
% Foster et al. (2010) PNAS 107:10815-10820
%
% Olaf Sporns, Indiana University, 2007/2008
% Vassilis Tsiaras, University of Crete, 2009
% Murray Shanahan, Imperial College London, 2012
% Mika Rubinov, University of Cambridge, 2012
if (flag==0) % undirected version
str = strengths_und(CIJ);
[i,j] = find(triu(CIJ,1)>0);
K = length(i);
stri = str(i);
strj = str(j);
else % directed versions
[is,os] = strengths_dir(CIJ);
[i,j] = find(CIJ>0);
K = length(i);
switch flag
case 1
stri = os(i);
strj = is(j);
case 2
stri = is(i);
strj = os(j);
case 3
stri = os(i);
strj = os(j);
case 4
stri = is(i);
strj = is(j);
end
end
% compute assortativity
r = ( sum(stri.*strj)/K - (sum(0.5*(stri+strj))/K)^2 ) / ...
( sum(0.5*(stri.^2+strj.^2))/K - (sum(0.5*(stri+strj))/K)^2 );
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