Re: [igraph] Clustering coefficient vs. transitivity

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

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. 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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