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iCAPs/packages/gspbox/graphs/gsp_erdos_renyi.m
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gsp_erdos_renyi.m
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function [ G ] = gsp_erdos_renyi( N,p,param )
%GSP_ERDOS_RENYI Create a random Erdos Renyi graph
% Usage: G = gsp_erdos_renyi( N,p,param );
% G = gsp_erdos_renyi( N,p );
%
% Input parameters:
% N : Number of nodes
% p : Probability of connection of a node with another
% param : Structure of optional parameter
% Output parameters:
% G : Graph structure.
%
% 'gsp_erdos_renyi( N,p,param )' initializes create a graph structure
% containing the weighted adjacency matrix (G.W), the number of vertices
% (G.N) for an Erdos Renyi graph. All edge weights are equal to 1.
%
% The Erdos Renyi graph is constructed by connecting nodes randomly. Each
% edge is included in the graph with probability p independent from every
% other edge.
%
% param a Matlab structure containing the following fields:
%
% param.connected : flag to force the graph to be connected. By
% default, it is 0.
%
% param.maxit : is the maximum number of try to connect the graph.
% By default, it is 10.
%
% param.verbose : 0 no log, 1 print main steps, 2 print all steps.
% By default, it is 1.
%
% Example:
%
% G = gsp_erdos_renyi(100,0.05)
%
% Url: http://lts2research.epfl.ch/gsp/doc/graphs/gsp_erdos_renyi.php
% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% If you use this toolbox please kindly cite
% N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
% and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
% ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781
% Author : Nathanael Perraudin
% Optional input arguments
if nargin<3, param=struct; end
if ~isfield(param, 'connected'), param.connected=0; end
if ~isfield(param, 'maxit'), param.maxit=10; end
if ~isfield(param, 'verbose'), param.verbose=1 ; end
% Check if the user didn't put silly parameter
if param.connected
if N*p<3
if param.verbose
fprintf(['The model has very low chance to create a '...
,'connected graph. Increase N, p or disable '...
,'param.connected \n']);
end
end
end
if p>1
error('The probability p cannot be above 1');
end
if p<0
error('The probability p cannot be negative');
end
% Create the graph structure
G=struct;
G.graph_type='erdos_renyi';
G.connected=param.connected;
% Create the graph
if param.connected
bool=0;
iter=1;
if param.verbose>1
fprintf('Entering the iteration process\n')
end
while ~bool
G.W = sprandsym(N, p)>0;
G.W(1:N+1:end) = 0;
bool=gsp_check_connectivity(G.W);
if iter==param.maxit
warning('The graph is not strongly connected.');
break;
elseif ~bool
if param.verbose>1
fprintf('Iteration %i failed. Trying again \n',iter)
end
iter=iter+1;
end
end
if param.verbose>1
if bool
fprintf('A connected graph has been created in %i iteration\n',iter);
else
fprintf('The iterative process has failed.\n');
end
end
else
G.W = sprandsym(N,p)>0;
G.W(1:N+1:end) = 0;
end
% try to create point to be associated with the points of the graph
% [x, y] = draw_dot(G.W);
%
%
% G.coords=[x',y'];
% G.limits=[-1e-4,1.01*max(x),-1e-4,1.01*max(y)];
G.type = 'erdos_renyi';
G = gsp_graph_default_parameters(G);
end
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