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iCAPs_v2/packages/gspbox/utils/gsp_resistance_distances.m
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gsp_resistance_distances.m
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function [resistance_distances] = gsp_resistance_distances(G,param)
%GSP_RESISTANCE_DISTANCES : Compute the resitance distances of a graph
% Usage: rd = gsp_resistance_distances(G);
% rd = gsp_resistance_distances(L);
%
% Input parameters:
% G : Graph structure or Laplacian matrix (L)
% param: optional parameters
% Output parameters:
% rd : distance matrix
%
% This function compute the resistance distances between all vertices in
% a graph. The distance between two nodes is defined as the inverse of
% the weight matrix. For example the distance matrix:
%
% dist = [0, 3, 1;...
% 3, 0, 2;...
% 1, 2, 0];
%
% corresponds to the weight matrix:
%
% W = [0, 1/3, 1/1;...
% 1/3, 0, 1/2;...
% 1/1, 1/2, 0];
%
% The function will compute the resistance distance following
% Kirshoff's law. In the our example it is:
%
% rd2 = [0, 3/2, 5/6;...
% 3/2, 0, 4/3;...
% 5/6, 4/3, 0]
%
% In matlab, you can reproduce this example using:
%
% % The weight
% dist = [0, 3, 1;...
% 3, 0, 2;...
% 1, 2, 0];
% % The weight is the inverse of the distance...
% W = dist.^(-1);
% % Fix the diagonal
% W([1,5,9])=0;
% G = gsp_graph(W);
% rd = gsp_resistance_distance(G)
% % Resitance computed by hand
% rd2 = [0, 3/2, 5/6;...
% 3/2, 0, 4/3;...
% 5/6, 4/3, 0]
%
% param is an optional structure that contains the following field
%
% param.verbose*: display parameter - 0 no log - 1 display warnings
% (default 1)
%
% References:
% D. J. Klein and M. Randic. Resistance distance. Journal of Mathematical
% Chemistry, 12(1):81--95, 1993.
%
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/utils/gsp_resistance_distances.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, David Shuman
% Testing: test_resistance_distance
if nargin < 2
param = struct;
end
if ~isfield(param,'verbose')
param.verbose = 1;
end
if isstruct(G)
% Use the non normalized laplacian
if ~strcmp(G.lap_type, 'combinatorial')
G = gsp_create_laplacian(G,'combinatorial');
if param.verbose
fprintf(['Compute the combinatorial laplacian ',...
'for the resitance distance\n']);
end
end
L = G.L;
if (isfield(G,'U') || isfield (G,'e') )
if issorted(G.e)
pseudo=G.U(:,2:G.N)*diag(1./G.e(2:G.N))*G.U(:,2:G.N)';
else
[e, si] = sort(G.e,'ascend');
U = G.U(:,si);
pseudo=U(:,2:G.N)*diag(1./e(2:G.N))*U(:,2:G.N)';
end
else
pseudo=pinv(full(L));
end
else
L = G;
pseudo=pinv(full(L));
end
N=size(L,1);
d = diag(pseudo);
resistance_distances = repmat(d,1,N) + repmat(d',N,1) - pseudo - pseudo';
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