

Community Detection in Graphs - scribu
http://jeremykun.com/2014/05/19/community-detection-in-graphs-a-casual-tour/

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j2kun
It's good to see my article on HN, but I have to admit it's woefully
incomplete.

I wrote the article a year ago, and I have continued to study community
detection through today. There are a number of large recent developments that
didn't make it into that post, particularly the methods based on the
_stochastic block model._ This model is sort of the simplest idea you can have
for a random graph with community structure: you specify the communities and
probabilities for within-community and across-community edges.

The nice thing about the SBM is that we have a very precise theoretical
understanding of when our best algorithms can and can't find the communities.
And moreover, our best algorithms are spectral algorithms (which look at
eigenvalues of the adjacency matrix of the network), which is another thing I
completely ignored in the post. We also happen to know that SBM is
particularly good for fitting to real data if that data has significant
community structure.

If you're interested in more of this stuff, check out the lecture notes of
Aaron Clauset[1] and in general the recent work of Mark Newman, Cris Moore,
etc.

[1]:
[http://tuvalu.santafe.edu/~aaronc/courses/5352/fall2013/](http://tuvalu.santafe.edu/~aaronc/courses/5352/fall2013/)

