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ISFCClustering/2019_03_03_BCT/clustering_coef_wu_sign.m
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clustering_coef_wu_sign.m
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function [C_pos,C_neg,Ctot_pos,Ctot_neg] = clustering_coef_wu_sign(W,coef_type)
%CLUSTERING_COEF_WU_SIGN Multiple generalizations of the clustering coefficient
%
% [C_pos,C_neg,Ctot_pos,Ctot_neg] = clustering_coef_wu_sign(W,coef_type);
%
% The weighted clustering coefficient is the average weight or intensity
% of all triangles associated with each node.
%
% Inputs:
% W,
% Weighted undirected connection matrix
%
% corr_type,
% Desired type of clustering coefficient.
% Options:
% 1, (default) Onnela et al. formula, used in original
% clustering_coef_wu.m. Computed separately for positive &
% negative weights.
% 2, Zhang & Horvath formula, similar to Onnela formula except
% denominator of Onnela formula relies on binarizing the
% network whereas this denominator is based on weight value,
% which reduces the sensitivity of this measure to the
% weights directly connected to the node of interest.
% Computed separately for positive & negative weights.
% 3, Constantini & Perugini's generalization of the Zhang &
% Horvath formula. This formula takes both positive &
% negative weights into account simultaneously, & is
% particularly sensitive to non-redundancy in path
% information based on sign (i.e., when two weights are
% positive & one negative, or all three are negative, both of
% which indicate that the weight of the third path is not
% redundant information). Produces only one value.
%
%
% Outputs:
% C_pos/C_neg,
% Clustering coefficient vector for positive/negative weights.
% For the third option, only one vector is outputted (as C_pos).
% Ctot_pos/Ctot_neg,
% Mean clustering coefficient for positive and negative weights.
%
% References:
% Onnela et al. (2005) Phys Rev E 71:065103
% Zhang & Horvath (2005) Stat Appl Genet Mol Biol 41:1544-6115
% Costantini & Perugini (2014) PLOS ONE 9:e88669
%
%
% Contributor: Jeff Spielberg, Boston University, 2014-2015
% (script based on clustering_coef_wu.m)
%
% Modification History:
% May 2014: Added computation of pos & neg weights separately &
% computation of mean coefficient (Jeff Spielberg)
% May 2015: Added computation of Zhang & Horvath and Constantini &
% Perugini formulas (Jeff Spielberg)
% May 2016: Bugfix in computation of the denominator of the Costantini &
% Perugini (flag 3) version (Chiara Pintossi)
if ~exist('coef_type','var')
coef_type = 1;
end
n = length(W); %number of nodes
W(1:n+1:end) = 0;
switch coef_type
case 1
W_pos = W.*(W>0);
K_pos = sum(W_pos~=0,2);
cyc3_pos = diag((W_pos.^(1/3))^3);
K_pos(cyc3_pos == 0) = inf; %if no 3-cycles exist, make C=0 (via K=inf)
C_pos = cyc3_pos./(K_pos.*(K_pos-1)); %clustering coefficient
Ctot_pos = mean(C_pos);
W_neg = -W.*(W<0);
K_neg = sum(W_neg~=0,2);
cyc3_neg = diag((W_neg.^(1/3))^3);
K_neg(cyc3_neg == 0) = inf; %if no 3-cycles exist, make C=0 (via K=inf)
C_neg = cyc3_neg./(K_neg.*(K_neg-1)); %clustering coefficient
Ctot_neg = mean(C_neg);
case 2
W_pos = W.*(W>0);
cyc3_pos = zeros(n,1);
cyc2_pos = zeros(n,1);
for i = 1:n
for j = 1:n
for q = 1:n
cyc3_pos(i) = cyc3_pos(i)+(W_pos(j,i)*W_pos(i,q)*W_pos(j,q));
if j~=q
cyc2_pos(i) = cyc2_pos(i)+(W_pos(j,i)*W_pos(i,q));
end
end
end
end
cyc2_pos(cyc3_pos == 0) = inf; %if no 3-cycles exist, make C=0 (via K=inf)
C_pos = cyc3_pos./cyc2_pos; %clustering coefficient
Ctot_pos = mean(C_pos);
W_neg = -W.*(W<0);
cyc3_neg = zeros(n,1);
cyc2_neg = zeros(n,1);
for i = 1:n
for j = 1:n
for q = 1:n
cyc3_neg(i) = cyc3_neg(i)+(W_neg(j,i)*W_neg(i,q)*W_neg(j,q));
if j~=q
cyc2_neg(i) = cyc2_neg(i)+(W_neg(j,i)*W_neg(i,q));
end
end
end
end
cyc2_neg(cyc3_neg == 0) = inf; %if no 3-cycles exist, make C=0 (via K=inf)
C_neg = cyc3_neg./cyc2_neg; %clustering coefficient
Ctot_neg = mean(C_neg);
case 3
cyc3 = zeros(n,1);
cyc2 = zeros(n,1);
for i = 1:n
for j = 1:n
for q = 1:n
cyc3(i) = cyc3(i)+(W(j,i)*W(i,q)*W(j,q));
if j~=q
cyc2(i) = cyc2(i)+abs(W(j,i)*W(i,q));
end
end
end
end
cyc2(cyc3 == 0) = inf; %if no 3-cycles exist, make C=0 (via K=inf)
C_pos = cyc3./cyc2; %clustering coefficient
Ctot_pos = mean(C_pos);
C_neg = nan(size(C_pos));
Ctot_neg = nan(size(Ctot_pos));
end
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