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Allowing communities to overlap is certainly desirable, though the methods 
that do that have other problems that make up for those advantages. 
(There definitely need to be better methods that allow overlap 
effectively...)  Some of the hard partitioning methods allow the 
consideration of things like overlap without doing overlap---e.g., a node 
could be assigned an assignment strength to multiple communities even if 
an algorithm only ultimately assigns it to one community.  Again, I think 
it would be good to look at some survey and review articles to see the 
pros and cons of various methods.

In terms of the Blondel method (often called Louvain method, btw) for 
optimizing modularity, you actually get better modularity values if you 
subsequently apply Kernighan-Lin steps.  (In fact, that's a good thing to 
do generally after one applies the various optimization techniques.) 
Again, though, I think tying oneself to one method rather than more 
thoroughly seeing the results of different methods---one can get nearly 
equal modularity values from rather different partitions (see Good et 
al)---so it's rather important to be cautious with this.

-----
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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