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## Re: [igraph] Clustering coefficient vs. transitivity

 From: Gábor Csárdi Subject: Re: [igraph] Clustering coefficient vs. transitivity Date: Tue, 6 Jul 2010 23:31:09 +0200

```Jonathan,

On Tue, Jul 6, 2010 at 7:30 PM, Jonathan Donges
> Dear Tamas,
> Thanks for the quick answer! Was transitivity_avglocal_undirected there from
> the beginning (early 0.5) or was it added later?

It was added somewhere around igraph 0.3, to the C core. It was added
to the python interface in 0.5.2, according to

> Was g.transitivity_undirected() referring to transitivity (Eq. 2.8) in all
> earlier versions, or might there have been a change at any time?

I doubt that there have been any change in this.

> Btw, I and my co-workers find the notation you use for the corresponding
> functions slightly misleading particularly for novices of network theory,
> since clustering coefficient is more commonly used for this measure.

As far as I know, this measure has been existed long before the term
"clustering coefficient" was coined, and it was already called
transitivity back then. This is the reason for the naming.

Best,
Gabor

> However, I think I understand your motivation, since you also have a
> clustering property referring to the graph's component structure etc.
> Cheers!
> Jonathan
> Am 06.07.2010 um 11:17 schrieb Tamas Nepusz:
>
> Dear Jonathan,
>
> I'm using igraph 0.6 via the Python interface. From some test cases I
>
> get the impression, that the function transitivity_undirected actually
>
> gives the mean value of transitivity_local_undirected. Is this
>
> correct?
>
> No; transitivity_avglocal_undirected is the mean value of
> transitivity_local_undirected. transitivity_undirected is indeed according
> to Eq.~(2.8) in the Boccaletti review; that is, 3 x (# of triangles) / (# of
> connected triplets):
>
> g = Graph.GRG(100, 0.2)
>
> g.transitivity_undirected()
>
> 0.63212
>
> g.transitivity_avglocal_undirected()
>
> 0.64516
>
> sum(g.transitivity_local_undirected())/g.vcount()
>
> 0.64516
>
> Also note that there are two possible ways to define
> transitivity_local_undirected(), depending on how vertices with degree less
> than two are treated. igraph can either treat them as havng zero local
> transitivity, or return NaN (not a number).
>
> --
> Tamas
>
>
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