gen_syn2.m

function [W_Cube, GT_Matrix, nbCluster]= gen_syn2(T,z,nbChange,state,blogSize,avgDegree,saveToFile)
% Generating the synthetic networks with 4 clusters,as described by Mark
% Newman's paper.
% Reference:
%   Newman M E J, Girvan M. Finding and evaluating community structure in networks[J].
%   Physical review E, 2004, 69(2): 026113.
%
% This generator is primarily implemented by Yu-Ru Lin (http://www.yurulin.com/download/code/facetnet.html).
%
%   INPUTS:
%       T: Number of time steps
%       z: Average number of edges of a node connecting to other clusters
%       nbChange: Number of nodes that switch membership at each time step
%       state: Initial state for random number generator
%       blogSize: Number of nodes in each graph, e.g., 128
%       avgDegree: Average degree of each node, e.g., 16
%       saveToFile: A boolean variable.To save the results to a mat file if
%       the value is true.
%
%    OUTPUTS:
%       W_Cube: A cell contains dynamic networks for T time steps. Each
%               network is represented by a matrix.
%       GT_Matrix: A cluster indicative matrix 
%       nbCluster: The number of clusters
%
%    sample usage:   gen_syn2(10,3,1,100,256,32)

if nargin == 6
    saveToFile = false;
elseif nargin < 6 || nargin > 7
    error('The number of parameters is not appropriate!');
end

rand('state', state);
randn('state', state);

nbCluster = 4; %the number of clusters is fixed to 4
clusterSize = blogSize/4;

p_out = z/(blogSize*3/4)
p_in = (avgDegree/2 - p_out*3*clusterSize)/(clusterSize -1) %to guarantee
%avgDegree, i.e., p_in*(clusterSize-1)+p_out*(3*clusterSize)=avgDegree/2
if ( p_in < p_out )
    input('Warning: p_in < p_out! Are you sure?');
end

GT = zeros(blogSize,nbCluster);
for i = 1:1:nbCluster
    start_idx = (i-1)*clusterSize+1;
    end_idx = i*clusterSize;
    GT(start_idx:end_idx, i) = 1;
end

W = unifrnd(0,1,blogSize,blogSize);
W2 = W;
WW2 = zeros(blogSize,blogSize);
WW2(W2 <= p_out) = 1;
W = WW2;
for i = 1:1:nbCluster
    start_idx = (i-1)*clusterSize+1;
    end_idx = i*clusterSize;
    W1 = unifrnd(0,1,clusterSize,clusterSize);WW1 = zeros(clusterSize,clusterSize);
    WW1(W1 <= p_in) = 1;W(start_idx:end_idx,start_idx:end_idx) = WW1;
end

W = W+W';
W(W>0)=1;
for i = 1:1:blogSize
    W(i,i) = 0;
end

W_Cube{1} = W;
GT_Cube{1} = GT;
c=zeros(clusterSize,4);
for i = 1:1:nbCluster
    start_idx = (i-1)*clusterSize+1;
    end_idx = i*clusterSize;
    cc(:,i) = start_idx:end_idx;
end

for kk=2:1:T

    W = unifrnd(0,1,blogSize,blogSize);
    W1 = W;
    W2 = W;
    WW1 = zeros(blogSize,blogSize);
    WW2 = zeros(blogSize,blogSize);
    WW1(W1 <= p_in) = 1;
    WW2(W2 <= p_out) = 1;
    W = WW2;
    for i = 1:1:nbCluster
        start_idx = (i-1)*clusterSize+1;
        end_idx = i*clusterSize;
        W(start_idx:end_idx,start_idx:end_idx) = WW1(start_idx:end_idx,start_idx:end_idx);
    end

    W = W+W';
    W(W>0)=1;
    for i = 1:1:blogSize
        W(i,i) = 0;
    end

    cc(:,1) = cc(randperm(clusterSize),1);
    cc(:,2) = cc(randperm(clusterSize),2);
    cc(:,3) = cc(randperm(clusterSize),3);
    cc(:,4) = cc(randperm(clusterSize),4);

    i = 1;
    cc(i:(i+nbChange-1),[2 3 4 1]') = cc(i:(i+nbChange-1),[1 2 3 4]');
    i = i+nbChange;
    cc(i:(i+nbChange-1),[3 4 1 2]') = cc(i:(i+nbChange-1),[1 2 3 4]');
    i = i+nbChange;
    cc(i:(i+nbChange-1),[4 1 2 3]') = cc(i:(i+nbChange-1),[1 2 3 4]');

    GT = zeros(blogSize,nbCluster);
    GT(cc(:,1),1) = 1;
    GT(cc(:,2),2) = 1;
    GT(cc(:,3),3) = 1;
    GT(cc(:,4),4) = 1;

    W([cc(:,1); cc(:,2); cc(:,3); cc(:,4)],:) = W;
    W(:,[cc(:,1); cc(:,2); cc(:,3); cc(:,4)]) = W;

    W_Cube{kk} = W;
    GT_Cube{kk} = GT;
end

GT_Matrix = zeros(blogSize, T);
for i=1:1:T
    GT_Matrix(:,i) = GT_Cube{i}*[1 2 3 4]';
end
% GT_Matrix
% spy(W_Cube{1})
fname = ['syn_T_' int2str(T) '_z_' int2str(z) '_nC_' int2str(nbChange) '_bS_' int2str(blogSize) '_aD_' int2str(avgDegree) '.mat'];
if (saveToFile)
    eval(['save ' fname  ' W_Cube GT_Cube GT_Matrix blogSize nbCluster T z nbChange blogSize avgDegree -mat -v7.3' ]);
end

end