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My first community detection e-mail of 2010... :)
There are a couple of issues to consider based on the question asked. One
is how to construct communities in the first place, and then there's your
cohesiveness measure. One thing that I'd strongly suggest is to do your
cohesiveness calculations using multiple methods of defining communities
to see how much things change. The results might not be robust with
respect to your definition (they probably won't be), so you're going to
need to be careful. The G-N betweenness-based method isn't going to be
your best choice (as has been pointed out), though the issue is
significantly broader than an implied one (from earlier in this thread)
about the application context of the network you're studying. It tends to
have trouble with highly-clustered networks, for instance.
In terms of which method to use, I can make further comments (I tend to be
a bit opinionated about this particular area), but aside from any private
correspondence with further details, let me just add a couple of hopefully
helpful articles to the mix:
1. I'll advertise my own survey/review article on community structure in
networks, which I think is a good place to get started on the topic
(obviously, I'm very biased about this) and see the layout of the land:
http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pdf
2. The article in (1) is a survey and as you're actually doing the
calculations, I think you'll also want to go to the following encyclopedic
review by Fortunato:
http://arxiv.org/abs/0906.0612
(you might want to check if the published version of this is now out; it
will come out pretty imminently)
I think my article is pretty user-friendly, so usually I recommend
starting there and then getting into the more technical articles.
As I mentioned, I'm happy to provide more info (and several of the
previous e-mails mentioned lots of good stuff), so let me know.
-----
Mason
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Mason A. Porter
University Lecturer (and Tutorial Fellow, Somerville College)
Oxford Centre for Industrial and Applied Mathematics
Mathematical Institute, University of Oxford
Homepage: http://www.maths.ox.ac.uk/~porterm, IM: tepid451
Blog: http://masonporter.blogspot.com/
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"I don't know. Maybe the knowledge of asymptotic analysis will lead
to less starvation among African children?"
--- Me, in an early draft of a grant proposal when asked to address
how the project will help with the socio-economic
development of third-world countries
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