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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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