Problem with newman_watts_strogatz_graph

[MINGXUAN HE]

Hi all,

I believe that the newman_watts_strogatz_graph function incorrectly implements this network model. In the current implementation, self-loops and multi-edges are not allowed. However the paper by Newman and Watts stated "we also explicitly allow there to be more than one bond between any two vertices, or a bond which connects a vertex to itself." The original contributor seems unsure by commenting "is that the correct NWS model?" 

The problem seemingly comes from an incorrect citation. Right now the reference used is:

Newman, M.E.J., Watts, D.J.: Renormalization group analysis of the small-world network model, Physics Letters A, 263, 341, 1999. https://doi.org/10.1016/S0375-9601(99)00757-4

which in fact uses the original Watts-Strogatz model, not the Newman-Watts variant.

The correct citation in which the Newman-Watts variant was proposed should be:

Newman, M.E.J., Watts, D.J.: Scaling and percolation in the small-world network model. Phys.Rev. E60(6), 7332–7342 (1999). DOI 10.1103/PhysRevE.60.7332

The aforementioned citation is in section II, paragraph 4 of the latter.

I guess the confusion might have come from these papers having the same in-text citation due to the exact same author and year.

To make sure it's not a difference in naming convention, I looked at several publications that uses the Newman-Watts model and confirmed they all uses the version that allows self-loops and multi-edges. But I hope someone can look into the references and double check for me. 

It would be easy to fix the code: when initializing the graph, set create_using to nx.multigraph(), and getting rid of the lines that rejects self-loops or multi-edges. I wrote the fixed code but I'm not sure how to upload it to the package, even after reading the contributor guide. (I'm a math student with no prior experience in large-scale collaborative development with git.) I wish someone can give me more instructions on that.

p.s. I recently implemented a generator for Klemm-Eguiluz networks. (ref: Klemm, Konstantin, and Victor M. Eguiluz. "Growing scale-free networks with small-world behavior." Physical Review E 65.5 (2002): 057102.) If I successfully figured out how to contribute via git I can share the code as a function under nx.generators.

Best,

Ming

[Dan Schult]

A good start to getting git going would be to add this email’s text to a “New Issue” on the GitHub repo.  HTTPS://github.com/NetworkX/NetworkX/issues

There is an optional template to fill out as part of the message, but you can erase that and put this text in for ease of entry.  Then you’ll need a GitHub account and you should make a “fork” of the NetworkX repo into your account.  The overall workflow is to move from your fork to your local machine where you write the code and then upload it to your repo. From there you can create a “pull request” from your repo to the NetworkX repo. That creates lots of nice tracking and testing tools which help us get it ready to “merge” and then we merge it.

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[MINGXUAN HE]

Thank you very much Dan!