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## Re: [igraph] Walktrap / Community / Modularity

 From: Amanda Schierz Subject: Re: [igraph] Walktrap / Community / Modularity Date: Tue, 17 Jul 2012 16:32:04 +0100 User-agent: Microsoft-MacOutlook/14.14.0.111121

```Hi
Just letting you know I applied this code successfully. I had to make a
slight amendment as igraph starts numbering from 0 (this effects the
contents of the adjlist) so I have added 1 to the adjlist contents before
doing the match,

sapply(1:vcount(g), function(v) { sum(membership[adjlist[[v]]+1] ==
membership[v]) / length(adjlist[[v]]) })

Many thanks
Mandy

On 06/07/2012 14:40, "Tamás Nepusz" <address@hidden> wrote:

>> 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.
>
>I am not aware of any formal definition for "vertex modularity", but an
>informal measure that some people have used is to count what fraction of
>the edges incident on the vertex stay inside the community. This can be
>calculated relatively easily.
>
>Suppose that you have a membership vector called "membership", and your
>graph is in "g". Then first we get the adjacency list of the graph:
>
>
>and then apply the following (pretty convoluted) expression:
>
>sapply(1:vcount(g), function(v) { sum(membership[adjlist[[v]]] ==
>membership[v]) / length(adjlist[[v]]) })
>
>Let's dissect the above expression a bit. sapply() takes two arguments;
>the first is a list, the second is a function. sapply() will call the
>function with each element of the list and store the values in a vector.
>The list we pass here is simply the list of vertex identifiers (from 1 to
>the number of vertices), and the function itself calculates the "vertex
>modularity" for a single vertex. In the function, we do the following.
>First, we take the neighbors of vertex v by calling adjlist[[v]] (note
>the double brackets), then fetch the community ids for each vertex:
>
>
>Then we compare each element of this vector with the community id of v
>itself:
>
>
>The result is a binary vector where TRUE means that a given neighbor is
>in the same community as v itself and FALSE means that it is not.
>Applying sum() to this vector gives us the number of neighbors that are
>in the same community as v, and dividing it by the number of neighbors
>gives us the number you are looking for.
>
>Best,
>T.
>
>
>
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