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Re: [igraph] Qualifying individual communities
From: |
Tamás Nepusz |
Subject: |
Re: [igraph] Qualifying individual communities |
Date: |
Tue, 4 Feb 2014 23:54:27 +0100 |
Hello,
> After computing a set of communities, using a multi-cut algorithm like
> infomap.community(), I understand it computes the modularity of the best
> (highest modularity) community.
Errrmm… not sure if we are completely on the same page here, so let me try to
clarify things and sorry if I’m stating the obvious.
First of all, modularity is a measure that quantifies the quality of a
community structure “as a whole”, so there is no such thing as the modularity
of a single community - the measure always refers to the quality of the entire
partition. Actually, the formula of the modularity measure can be rearranged
such that the outermost sum in the formula iterates over each of the
communities one by one, so one could theoretically say that whatever is within
the outermost sum is the modularity of an individual community, but the problem
is that the individual contributions of the communities to the modularity score
as a whole are not normalized; larger communities contribute more to the
modularity score than small ones.
If you are looking for a measure that helps you to select the “important”
communities out of a community structure that infomap.community or whatever
other algorithm gives to you, read the following paper - I think it’s a good
starting point:
http://arxiv.org/abs/0907.3708
The measure that the authors describe in this paper is not implemented in
igraph, but they seem to provide their own implementation.
All the best,
Tamas