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ISFCClustering/2019_03_03_BCT/randmio_und_signed.m
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randmio_und_signed.m
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function [R,eff] = randmio_und_signed(W, ITER)
% RANDMIO_UND_SIGNED Random graph with preserved signed degree distribution
%
% R = randmio_und_signed(W,ITER);
% [R,eff] = randmio_und_signed(W,ITER);
%
% This function randomizes an undirected network with positively and
% negatively signed connections, while preserving the positively and
% negatively signed degree distribution. The function does not preserve
% the strength distribution in weighted networks.
%
% Input: W, undirected (binary/weighted) connection matrix
% ITER, rewiring parameter
% (each edge is rewired approximately ITER times)
%
% Output: R, randomized network
% eff, number of actual rewirings carried out
%
% Reference: Maslov and Sneppen (2002) Science 296:910
%
%
% 2011-2015
% Dani Bassett, UCSB
% Olaf Sporns, Indiana U
% Mika Rubinov, U Cambridge
% Modification History:
% Mar 2011: Original (Dani Bassett, based on randmio_und.m)
% Mar 2012: Limit number of rewiring attempts,
% count number of successful rewirings (Olaf Sporns)
% Dec 2015: Rewritten the core of the rewiring algorithm to allow
% unbiased exploration of all network configurations. The new
% algorithm allows positive-positive/negative-negative
% rewirings, in addition to the previous positive-positive/0-0
% and negative-negative/0-0 rewirings (Mika Rubinov).
if nargin('randperm')==1
warning('This function requires a recent (>2011) version of MATLAB.')
end
R = double(W); % sign function requires double input
n = size(R,1);
ITER = ITER*n*(n-1)/2;
% maximal number of rewiring attempts per 'iter'
maxAttempts = round(n/2);
% actual number of successful rewirings
eff = 0;
for iter=1:ITER
att=0;
while (att<=maxAttempts) %while not rewired
%select four distinct vertices
nodes = randperm(n,4);
a = nodes(1);
b = nodes(2);
c = nodes(3);
d = nodes(4);
r0_ab = R(a,b);
r0_cd = R(c,d);
r0_ad = R(a,d);
r0_cb = R(c,b);
%rewiring condition
if (sign(r0_ab)==sign(r0_cd)) && ...
(sign(r0_ad)==sign(r0_cb)) && ...
(sign(r0_ab)~=sign(r0_ad))
R(a,d)=r0_ab; R(a,b)=r0_ad;
R(d,a)=r0_ab; R(b,a)=r0_ad;
R(c,b)=r0_cd; R(c,d)=r0_cb;
R(b,c)=r0_cd; R(d,c)=r0_cb;
eff = eff+1;
break;
end %rewiring condition
att=att+1;
end %while not rewired
end %iterations
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