Re: [igraph] Qualifying individual communities

[Tamás Nepusz]

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