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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.
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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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