[igraph] Re: igraph doubt

[Tamas Nepusz]

Dear Sushma,

I'm cc-ing this email to the igraph mailing list. Please consider subscribing 
to the mailing list and asking questions there instead of writing directly to 
me -- chances are that you get faster answers on the mailing list than by 
writing to me privately.

> I have tried out initially the leading eigen vector method of community 
> detection using the network given in the original paper of Newman ,karate 
> club network and i found out the number of communities that i have got are 
> more(5) than that of actually(4) present.
Which one is the original paper you are referring to? In igraph, we used the 
following paper:

MEJ Newman: Finding community structure in networks using the eigenvectors of 
matrices, Phys Rev E 74:036104, 2006.

This paper contains no results regarding the Zachary karate club network, so I 
cannot compare igraph's results against it at the moment. I've also checked 
another paper of Newman, which does include a short analysis of the Zachary 
karate club network with the leading eigenvector method, but it only reports a 
subdivision into two communities after the first split:

MEJ Newman: Modularity and community structure in networks. PNAS 
103:8577--8582, 2006.

Incidentally, this split matches the one provided by igraph if you request only 
two communities from the leading eigenvector method.

> Will you please let  me  know what the reason might be ??
Well, my question is why do you think that there are only 4 real communities in 
the network? Various community detection algorithms applied to the Zachary 
karate club network may detect 2, 3, 4, 5 or more communities -- it all depends 
on which method do you use (and with what parameters). Sure, for the Zachary 
karate club network, one can actually show that the subdivision with the 
highest modularity score (0.4197) has four communities, but since there is no 
external ground truth against which we can validate the communities, this does 
not mean that there are four "real" communities in the network. It all depends 
on how you define communities. If you define the communities as the groups 
corresponding to the subdivision with the maximal modularity score, then yes, 
there are four communities in the networks, but none of the actual community 
detection methods are guaranteed to find that optimal configuration -- they are 
just heuristics.

> Can you please let me know where  i can   get the detailed code of this 
> igraph function??
You can download igraph's source code from its Sourceforge page:

http://igraph.sourceforge.net/download.html

You can also browse the source code on igraph's Launchpad page. The source code 
of the leading eigenvector function is here:

http://bazaar.launchpad.net/%7Eigraph/igraph/0.5-main/annotate/head%3A/src/community.c#L1082

-- 
Tamas