Re: [igraph] Walktrap / Community / Modularity

[Gábor Csárdi]

Hi Amanda,

how exactly is vertex modularity defined? Do you have a reference?

Gabor

On Fri, Jul 6, 2012 at 4:47 AM, Amanda Schierz <address@hidden> wrote:
> Hi.
>
> Thanks for your reply. Do you know if there is a way I can calculate vertex 
> modularity? I want to know how modular a vertex is - ie. does its edges stay 
> within the community or cross communities - is it a hub of the community or 
> is it the community/rest of graph communicator.
>
> thanks
> ________________________________________
> From: address@hidden address@hidden On Behalf Of Tamás Nepusz address@hidden
> Sent: 05 July 2012 22:50
> To: Help for igraph users
> Subject: Re: [igraph] Walktrap / Community / Modularity
>
> Hi,
>
>> I have a network with approx 9500 vertices. The vertices are labelled from 0 
>> upwards. I ran Walktrap.communities and have the membership vector. I then 
>> ran Modularity on the walktrap object and a vector was returned the same 
>> length as the number of vertices. I therefore assume these are vertex 
>> modularity scores.
> No, they aren't. Modularity refers to the "quality" of a partition with 
> respect to the whole network. The reason why you may be getting a vector is 
> because walktrap is a hierarchical clustering method, i.e. it merges pairs of 
> vertices or communities progressively, and the modularity vector returns the 
> modularity of the partition after _each_ merge. The correlation you see is 
> purely artificial: since merging pairs of vertices tends to increase the 
> modularity of the partition (when the algorithm is doing its job properly and 
> selects the right pair of vertices or communities in each step), the 
> modularity score will increase for a long while, then have a peak somewhere 
> (which one may use to select where to cut the dendrogram that the walktrap 
> algorithm generates), then drop back to zero.
>
> Best,
> T.
>
>
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-- 
Gabor Csardi <address@hidden>     MTA KFKI RMKI