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ISFCClustering/2019_03_03_BCT/edge_nei_overlap_bd.m
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edge_nei_overlap_bd.m
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function [EC,ec,degij] = edge_nei_overlap_bd(CIJ)
% EDGE_NEI_OVERLAP_BD Overlap amongst neighbors of two adjacent nodes
%
% [EC,ec,degij] = edge_nei_bd(CIJ);
%
% This function determines the neighbors of two nodes that are linked by
% an edge, and then computes their overlap. Connection matrix must be
% binary and directed. Entries of 'EC' that are 'inf' indicate that no
% edge is present. Entries of 'EC' that are 0 denote "local bridges",
% i.e. edges that link completely non-overlapping neighborhoods. Low
% values of EC indicate edges that are "weak ties".
%
% If CIJ is weighted, the weights are ignored. Neighbors of a node can be
% linked by incoming, outgoing, or reciprocal connections.
%
% Inputs: CIJ, directed (binary/weighted) connection matrix
%
% Outputs: EC, edge neighborhood overlap matrix
% ec, edge neighborhood overlap per edge, in vector format
% degij, degrees of node pairs connected by each edge
%
% Reference:
%
% Easley and Kleinberg (2010) Networks, Crowds, and Markets.
% Cambridge University Press, Chapter 3
%
% Olaf Sporns, Indiana University, 2012
[ik,jk,ck] = find(CIJ);
lel = length(ck);
N = size(CIJ,1);
[~,~,deg] = degrees_dir(CIJ);
ec = zeros(1,lel);
degij = zeros(2,lel);
for e=1:lel
neiik = setdiff(union(find(CIJ(ik(e),:)),find(CIJ(:,ik(e))')),[ik(e) jk(e)]);
neijk = setdiff(union(find(CIJ(jk(e),:)),find(CIJ(:,jk(e))')),[ik(e) jk(e)]);
ec(e) = length(intersect(neiik,neijk))/length(union(neiik,neijk));
degij(:,e) = [deg(ik(e)) deg(jk(e))];
end;
ff = find(CIJ);
EC = 1./zeros(N);
EC(ff) = ec; %#ok<FNDSB>
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