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## Re: [igraph] calculate vertices statistical features like degree eccentr

 From: Gábor Csárdi Subject: Re: [igraph] calculate vertices statistical features like degree eccentricity etc Date: Tue, 24 Jun 2014 10:25:32 -0400

```On Tue, Jun 24, 2014 at 10:14 AM, Csaba Ragany <address@hidden> wrote:
> Thank you!
>
> I have some further questions:
>
> 1) Is it possible to calculate the triangle count by vertices?

Search http://igraph.org/r/doc/ for 'triangle'

> 2) I think stress centrality is the number of shortest paths through a
> vertice, and betweenness is some kind of "probability" of shortest paths by
> vertices (exact definition here:
> http://med.bioinf.mpi-inf.mpg.de/netanalyzer/help/2.6.1/#nodeBetween ). So
> igraph's betweenness() stands for what?

Betweenness is exactly the number of shortest paths passing through
the vertex, at least this is how it is implemented in igraph, and this
seems to be the "correct" definition:
http://en.wikipedia.org/wiki/Betweenness_centrality

> 3) There are several statistical features that uses the shortest paths
> length like eccentricity(), betweenness(), closenes() etc. What happens if I
> want to calculate all these features to all vertices in a huge graph having
> ~300.000 nodes? Is there a way to calculate the sortest paths only once or
> how can I be more effective?

Is this a theoretical questions? The answer is no, there is no way in
igraph, but it is very easy in R once you have the lengths. Except for
betweenness() that needs the actual paths, not just the lengths.

In practice, it takes a while to calculate 9e+10 shortest paths to
store, so I am not sure this is feasible. You also need about
720GBytes of memory to store them.

Gabor

>
> Thank you!
> Csaba
>
>
>
> 2014-06-20 16:45 GMT+02:00 Gábor Csárdi <address@hidden>:
>
>> Hi,
>>
>> On Fri, Jun 20, 2014 at 10:38 AM, Csaba Ragany <address@hidden> wrote:
>> > Dear All,
>> >
>> > I want to calculate some statistical features on vertices like degree,
>> > eccentricity etc. I found lots of features on the internet but I some of
>> > them are not implemented in igraph or I did not find the appropriate
>> > function...
>> >
>> > So can you tell me how to calculate the below statistical features in
>> > igraph
>> > or is it possible?
>> > - neighborhood connectivity
>>
>> graph.knn()?
>>
>> > - topological coefficient
>>
>> AFAIK not implemented.
>>
>> > - degree centrality
>>
>> degree()
>>
>> > - stress centrality
>>
>> betweenness()?
>>
>> > - Katz centrality
>>
>> AFAIK not implemented.
>>
>> Gabor
>>
>> >
>> > Thank you!
>> > Csaba
>> >
>> > _______________________________________________
>> > igraph-help mailing list
>> > https://lists.nongnu.org/mailman/listinfo/igraph-help
>> >
>>
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