function [node,ncluster,nedges] = choose_node( G, nset, nsize )
%function [node,ncluster,nedges] = choose_node( G, nset, nsize )
%
% Choose the node that causes the least number of edges to be added to 2b,
N = length(nset);
clusters = cell(1,N);
newedges = cell(1,N);
numedges = zeros(1,N);
for i=1:N,
  v = nset(i);
  clusters{i} = induced_cluster( v, G );
  newedges{i} = new_edges( clusters{i}, G );
  numedges(i) = length(newedges{i});
end;
% breaking ties by choosing the node that induces the cluster with the smallest
% weight.
posnodes = zeros(1,N);
[num,varindex]=min(numedges);
posnodes(varindex) = 1;
numedges(varindex) = N*N; % largest possible
while 1,
  [val,varindex]=min(numedges);
  if val > num,
    break;
  else
    posnodes(varindex) = 1;
    numedges(varindex) = N*N; % largest possible
  end;
end;
smallest = find(posnodes);
N = length(smallest);
if N > 1,
  weights = zeros(1,N);
  for i=1:N,
    var = smallest(i);
    weights(i) = calc_weight( clusters{var}, nsize );
  end;
  [wgt,vari]=min(weights);
  node = smallest(vari);
else
  node = smallest;
end;
ncluster = clusters{node};
nedges   = newedges{node};