Re: [igraph] Qualifying individual communities

[A. Gerow]

Thanks Tamas -

That paper is a great help -- it may redirect my analysis a bit.

What confused me was the description of the membership function, namely for hierarchical algorithms like infomap:

"membership gives the division of the vertices, into communities. It returns a numeric vector, one value for each vertex, the id of its community. Community ids start from one. Note that some algorithms calculate the complete (or incomplete) hierarchical structure of the communities, and not just a single partitioning. For these algorithms typically the membership for the highest modularity value is returned, but see also the manual pages of the individual algorithms."

This implies there are multiple modularity values used not only to nest the clusters but to measure their individual modularity to construct a dendrogram. Perhaps these are some other scores? Or maybe I am thinking about a partition in the wrong way...

- A

On 4 February 2014 16:54, Tamás Nepusz <address@hidden> wrote:

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

--

A. Gerow

Knowledge Lab | Computation Institute

University of Chicago
5735 South Ellis Avenue
Chicago, IL 60637 - USA