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ISFCClustering/2019_03_03_BCT/latmio_dir_connected.m
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latmio_dir_connected.m
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function [Rlatt,Rrp,ind_rp,eff] = latmio_dir_connected(R,ITER,D)
%LATMIO_DIR_CONNECTED Lattice with preserved in/out degree distribution
%
% [Rlatt,Rrp,ind_rp,eff] = latmio_dir_connected(R,ITER,D);
%
% This function "latticizes" a directed network, while preserving the in-
% and out-degree distributions. In weighted networks, the function
% preserves the out-strength but not the in-strength distributions. The
% function also ensures that the randomized network maintains
% connectedness, the ability for every node to reach every other node in
% the network. The input network for this function must be connected.
%
% Input: R, directed (binary/weighted) connection matrix
% ITER, rewiring parameter
% (each edge is rewired approximately ITER times)
% D, distance-to-diagonal matrix
%
% Output: Rlatt, latticized network in original node ordering
% Rrp, latticized network in node ordering used for
% latticization
% ind_rp, node ordering used for latticization
% eff, number of actual rewirings carried out
%
% References: Maslov and Sneppen (2002) Science 296:910
% Sporns and Zwi (2004) Neuroinformatics 2:145
%
% Mika Rubinov, UNSW, 2007-2010
% Olaf Sporns, Indiana University, 2012
n=size(R,1);
% randomly reorder matrix
ind_rp = randperm(n);
R = R(ind_rp,ind_rp);
% create 'distance to diagonal' matrix
if nargin<3 %if D is not specified by user
D=zeros(n);
u=[0 min([mod(1:n-1,n);mod(n-1:-1:1,n)])];
for v=1:ceil(n/2)
D(n-v+1,:)=u([v+1:n 1:v]);
D(v,:)=D(n-v+1,n:-1:1);
end
end
%end create
[i,j]=find(R);
K=length(i);
ITER=K*ITER;
% maximal number of rewiring attempts per 'iter'
maxAttempts= round(n*K/(n*(n-1)));
% actual number of successful rewirings
eff = 0;
for iter=1:ITER
att=0;
while (att<=maxAttempts) %while not rewired
rewire=1;
while 1
e1=ceil(K*rand);
e2=ceil(K*rand);
while (e2==e1)
e2=ceil(K*rand);
end
a=i(e1); b=j(e1);
c=i(e2); d=j(e2);
if all(a~=[c d]) && all(b~=[c d])
break %all four vertices must be different
end
end
%rewiring condition
if ~(R(a,d) || R(c,b))
%lattice condition
if (D(a,b)*R(a,b)+D(c,d)*R(c,d))>=(D(a,d)*R(a,b)+D(c,b)*R(c,d))
%connectedness condition
if ~(any([R(a,c) R(d,b) R(d,c)]) && any([R(c,a) R(b,d) R(b,a)]))
P=R([a c],:);
P(1,b)=0; P(1,d)=1;
P(2,d)=0; P(2,b)=1;
PN=P;
PN(1,a)=1; PN(2,c)=1;
while 1
P(1,:)=any(R(P(1,:)~=0,:),1);
P(2,:)=any(R(P(2,:)~=0,:),1);
P=P.*(~PN);
PN=PN+P;
if ~all(any(P,2))
rewire=0;
break
elseif any(PN(1,[b c])) && any(PN(2,[d a]))
break
end
end
end %connectedness testing
if rewire %reassign edges
R(a,d)=R(a,b); R(a,b)=0;
R(c,b)=R(c,d); R(c,d)=0;
j(e1) = d; %reassign edge indices
j(e2) = b;
eff = eff+1;
break;
end %edge reassignment
end %lattice condition
end %rewiring condition
att=att+1;
end %while not rewired
end %iterations
% lattice in node order used for latticization
Rrp = R;
% reverse random permutation of nodes
[~,ind_rp_reverse] = sort(ind_rp);
Rlatt = Rrp(ind_rp_reverse,ind_rp_reverse);
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