function y = peripheral_node(A)
% function y = peripheral_node(A)
% given a square, sparse symmetric matrix A, find the
% pesudo-peripheral node using the Algorithm by George and Liu.
% NB. I need to explain what a peripheral node is later.

L_old = 0;
L_new = 1;

[M,N] = size(A);


link = zeros(M,1);
for k = 1:M
  link(k) = sum(A(k,:)~=0) - 1;
end

[Y,I] = sort(link);

x = I(end); % pick initial guess

% pick a random starting node
% x = ceil(M*rand);

while (L_new > L_old)
  L_old = L_new;

  % create the tree
  l{1} = x;

  % create test vector
  e = zeros(1,M);
  e(l{1}) = 1;

  % set counter variables
  k = 2; n = 1; 

  while (sum(e>0) < M)
    % initialize next tree
    l{k} = [];
    for j = 1:n
      v = (A(l{k-1}(j),:)~=0);
      % store new level.  This is actually redundant because
      % all we care about is the last level which gives us the
      % pseudo peripheral node.  
      l{k} = [l{k} find((v-e)>0)];
      e = e+v;
      e = (e~=0);
      % stop loop if we've found all links
      if (sum(e>0) == M)
        j = n;
      end
    end
    [m,n] = size(l{k});
    % if no new links are found, stop loop.
    if (n == 0)
      e = ones(1,M);
      k = k-1; % needed for accounting purposes
    end
    k = k+1;
  end
  L_new = k-1;

  [Y,I]=sort(l{L_new});
  x = l{L_new}(I(1));

end


y = l{1};