[Question] Running Leiden community detection on random graph generates multiple communities about graspologic

[johandahlberg]

Thank you for your quick and useful answer @bdpedigo! I'll look further into the methods you suggest.

[bdpedigo]

Absolutely - if it's alright with you I'm going to close this issue since I don't think there's anything to be done in terms of graspologic, but please feel free to post any further questions here.

[bdpedigo]

Hi @johandahlberg - unfortunately, this is a known issue with Leiden as well as other modularity maximization methods. These methods aren't doing model selection, and aren't good at "knowing" when the community structure they find is significant or would be expected under a random model as you point out. See for instance in this image of an adjacency matrix after sorting by the partition inferred by Leiden (from https://bdpedigo.github.io/networks-course/community_detection.html#overfitting):

You'll notice that those "communities" actually do have more within-community connections than without, so these structures can actually pop up just by chance.

One option is to explicitly form a null distribution (say, sampling a few hundred ER graphs, running Leiden, and computing the modularity) and then comparing your results to such a distribution.

Zhang and Peixoto also wrote this nice article about this problem https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.043271 and provide an alternative formulation that relies on a variant of the stochastic block model. Their implementation is in graph-tool here. The tradeoff is I'm guessing it's slower, might be harder to optimize, etc. but could be helpful for your application so I thought I'd mention it.