Fixes #5012 implementation of newman watts strogatz graph inconsistent with model

[mingxuan-he]

This PR fixes issue #5012 by modifying the implementation to allow multi-edges and self-loops in the model. The description for the Newman-Watts-Strogatz algorithm can be found in: Newman, M.E.J., Watts, D.J.: Scaling and percolation in the small-world network model. Phys.Rev. E60(6), 7332–7342 (1999). https://doi.org/10.1103/PhysRevE.60.7332

Also adds a simple test for the other extreme case p=1.

[dschult]

I have looked into this description and agree with many items. The newly cited paper provides a better description of how to handle the question of selfloops and multiedges than the current citation in NetworkX. Unfortunately it is also different from our current function and that will cause backward incompatibility. Note that the current implementation is not incorrect given the less precise description in the currently cited paper. I also notice that the name involves 3 authors and neither paper is written by strogatz.

I suggest that we implement this change as follows:

• retain the current function newman_watts_strogatz_graph and add words in the doc_string to describe how self-loops and multiedges are avoided. It should also "see also" the new function described next.
• create a new function (perhaps newman_watts_graph ?) that returns a MultiGraph and handles the selfloops and multiedges as in the cited paper suggested by this PR.

What do you think? It avoids backward incompatibility by keeping the simple graph interpretation available, yet makes the analytically tractable version available too.

[mingxuan-he]

That's a great suggestion! I'll work on it

[rossbar]

Gentle ping @mingxuan-he - are you still working on this one?

[MridulS]

@mingxuan-he thanks for the PR!

This hasn't been touched in a while. I'll go ahead and close this. Feel free to send a new PR :)
Thanks!