Discrepancy between Graph.modular_decomposition() and Wikipedia
I am either confused, or am seeing a bug, or there's a bug on Wikipedia.
There's a diagram on the page about modular decomposition referenced by the docs: http://en.wikipedia.org/wiki/Modular_... http://en.wikipedia.org/wiki/File:Mod...
It shows a 'series' module containing 2,3,4.
But when I recreate that graph and run modular_decomposition() on it I get something that seems different:
W = Graph() W.add_edges([[1,2],[1,4],[1,3],[2,4],[2,5],[2,6],[2,7],[3,4],[3,5],[3,6],[3,7],[4,5],[4,6],[4,7],[5,6],[5,7],[6,8],[6,9],[6,10],[6,11],[7,8],[7,9],[7,10],[7,11],[8,9],[8,10],[8,11],[9,10],[9,11]]) W.plot(vertex_size=100) W.modular_decomposition()
results in
('Prime', [ ('Serie', [ ('Parallel', [ 10, 11 ] ), 9, 8 ] ), ('Parallel', [ 6, 7 ] ), 5, 1, 4, ('Parallel', [ 2, 3 ] ) ] )
Which shows 8,9,10,11 in a 'series' but not 2,3,4.
Am I getting something wrong or missing something?
I agree that (2,3,4) is a module, and that sage isn't saying so. I think it's a bug. If you have an account on trac, I suggest opening a ticket. If you don't, I would encourage you to request a trac account.