Compute the condensed graph of A

condense.m

function [B,compindex,ci]=condense(A)
% CONDENSE Construct the condensed graph of A
%    
%    [B,compindex,ci] = condense(A) returns the 
%    condensed graph of A.
%
%    Example: 
%       A = zeros(5,5);
%       A(1,2) = 1; A(2,3) = 1; A(3,4) = 1; A(4,2) = 1; A(4,5) = 1; 
%       [B,compindex] = condense(A)
%
%    See also COMPONENT

if ~issparse(A)
    B = sparse(A);
else
    B = A;
end

num_nodes = size(B,1);

[ci,sizec] = components(B); 

if any(sizec >= 2) 
    
    num_components = max(ci);
    R = sparse(1:num_nodes,ci,1,num_nodes,num_components);
    B = R'*A*R;
    B = B - diag(diag(B));
    
    % construct component index 
    % compindex{i} = [u v]  if nodes u and v are in component i
    compindex = cell(num_components,1);
    for c = 1:num_components 
        compindex{c} = find(ci==c);
    end
else
    B = A; 
    compindex = num2cell(1:num_nodes);
end