function g = goodorder(G,sig)
% an odering sigma induces a sequence of subgraphs
% a subgraph G_i is faithful to G if for each v,u in G_i
% (path from v to u in G) ==> (path from v to u in G_i)
% the odering is good if each of the sigma-subgraphs is faithful to G

% G is a symmetric 0-1 matrix

[n,n] = size(G);
for i=1:n
  Gi = build_subgraph(G,sig,i);
  g = is_faithful(G,Gi);
  if ~g
    return
  end
end
return

function b = is_faithful(G,Gi)
[nodesi,nodesj]=find(G);
ii = find(nodesi<nodesj);
nodesi = nodesi(ii);
nodesj = nodesj(ii);

for j=1:i
  for k=1:i
    u = sig(j);
    v = sig(k);
    Gi(u,v) = G(u,v);
  end
end
return



function Gi = build_subgraph(G,sig,i)
Gi = zeros(size(G));
for j=1:i
  for k=1:i
    u = sig(j);
    v = sig(k);
    Gi(u,v) = G(u,v);
  end
end
return