function p = rcm(A)
% function p = rcm(A)
% Reverse Cuthill-Mckee Algorithm for minimizing envelope profile
% Input is expected to be some symmetric matrix A, though this
% algorithm still works for a non symmetric matrix.

[M,N] = size(A);
p = zeros(M,1);

e = spalloc(1,N,N); % vector for storing which nodes have been
                    % labelled.  If e(k) = 1, node k has been
                    % labelled.If e(k) = 0, node k has not been labelled.
		      
% remove single unconnected nodes
for k = 1:M
  deg = sum(abs(A(k,:))>0) - 1; % check kth row of A
  if (deg == 0)
    p(N) = k;
    e(k) = 1;
    N = N-1;
  end
end


% main loop
while (N>0)  % in case the graph is not connected
  nz = find(e==0);
  k = peripheral_node(A(nz,nz));
  k = nz(k);
  e(k) = 1;
    
  v = [k];
  [m,n] = size(v);
  
  
  while(n>0)
    k = v(1);
    t =  find(((abs(A(k,:))>0) - e)>0);  % find all adjacent nodes S
                                         % to node k that are not yet
                                         % labelled
    [mt,nt] = size(t);  % sort through unlabelled adjacent S nodes
    deg = zeros(1,nt);  
    for j = 1:nt
      deg(j) = sum(abs(A(t(j),:))>0) - 1;
    end
    [Y,I] = sort(deg);
    v = [v t(fliplr(I))];    % update labelled nodes with S sorted
                             % in max deg
    e = e + (abs(A(k,:))>0); % label the adjacent nodes S as labelled
    e = (e>0);               % reinitialize to ones and zeros.
    
    p(N) = v(1);
    N = N-1;
    v = v(2:end);
    [m,n] = size(v);
  end
end