Added chodal_simplicial_vertex function

[hector1618]

I have added small function to get simplicial vertex for chordal graph.

Main objective is to get some preliminary code review before further work.

[dschult]

The main loop uses nx.all_neighbors, but you have restricted the routine to undirected graphs so might be better to use G[node] to get neighbors. So the main loop could become:

for node in G:
     if _is_complete_graph(G.subgraph(G[node])):
        return node

Note also that some "corner" cases may exist.. I think isolated nodes might be found by this routine. Maybe that is OK... I don't know enough about the applications. Similarly, nodes of degree 1 would qualify.

You should spell check the doc_string.
The tests could be expanded to include making sure the error(NetworkXError) behavior is correct.

Thanks!

[SanketDG]

Use the decorator @not_implemnted_for('directed','multigraph') here. This will raise NetworkXNotImplemented, which seems much more relevant.

[SanketDG]

Better, if this could be added to is_chordal function instead.

[hector1618]

Thank you for reply @dschult and @SanketDG.

Vertices with degree at most one can be considered as simplicial vertices. These definition will be useful while creating the pre-vertex ordering for Chordal graphs (both for disconnected and connected).

I second with @SanketDG that Not_implemented_for should be for is_chordal if we are not planning to handle directed chordal graph soon.

[jfinkels]

Use from networkx.utils import not_implemented_for instead.

[hagberg]

Needs updating to address comments.

[MridulS]

This hasn't been updated in a while, I'll go ahead and close this PR. Thanks for your work on this @hector1618 !