Re: [igraph] Clustering coefficient vs. transitivity

[Jonathan F. Donges]

Gabors and Tamas,

Thanks for the information. Due to the potential for
misinterpretation, I would strongly suggest that you include more
explicit warnings, maybe even references to the literature (Newman,
Boccaletti) in the DOCSTRINGS of both transitivity_undirected and
transitivity_avglocal_undirected. The clustering coefficient
(Watts-Strogatz or "true" transitivity) is among the most frequently
used measures of network theory and most researchers (most of which
have not been in the field before due to its exponential growth)
probably know it nowadays as "clustering coefficient" from the newer
literature.

Best wishes,
Jonathan

2010/7/6 Gábor Csárdi <address@hidden>:
> Jonathan,
>
> On Tue, Jul 6, 2010 at 7:30 PM, Jonathan Donges
> <address@hidden> wrote:
>> 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
> http://bazaar.launchpad.net/~igraph/igraph/0.6-main/annotate/head:/interfaces/python/src/graphobject.c
>
>> 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
>>
>>
>> _______________________________________________
>> igraph-help mailing list
>> address@hidden
>> http://lists.nongnu.org/mailman/listinfo/igraph-help
>>
>>
>> _______________________________________________
>> igraph-help mailing list
>> address@hidden
>> http://lists.nongnu.org/mailman/listinfo/igraph-help
>>
>>
>
>
>
> --
> Gabor Csardi <address@hidden>     UNIL DGM
>
> _______________________________________________
> igraph-help mailing list
> address@hidden
> http://lists.nongnu.org/mailman/listinfo/igraph-help
>