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Matthew -- I think you'll find the following article really helpful:

Newman, M. E. J. (2003) "The structure and function of complex networks,"
     SIAM Review (45) 2, pp. 167-256.
     http://epubs.siam.org/sam-bin/getfile/SIREV/articles/42480.pdf

See section 3.2 in particular (page 17 of the PDF, page 183 of the
article). Newman talks about two different clustering coefficient
formulas, which he refers to as C(1) and C(2).

Newman notes that the Watts & Strogatz definition, C(2), tends to
weight low-degree nodes more heavily than C(1).

That leads me to a follow-up question: Can anyone on the list offer
guidance as to what situations either measure is more appropriate
for??


Steven L. Johnson
Ph.D. Student, Information Technology
University of Maryland Smith School of Business
http://www.wam.umd.edu/~stevenlj/
What a gmail account? Send me a request.


On Wed, 12 Jan 2005 15:44:54 +0000, Matthew Vernon
<[log in to unmask]> wrote:
> *****  To join INSNA, visit http://www.insna.org  *****
>
> Hello,
>
> I have a query regarding clustering coefficients. Watts and Strogatz[1]
> define it as follows:
>
> "Suppose that a vertex v has kv neighbours; then at most kv(kv-1)/2
> edges can exist between them (this occurs when every neighbour of v is
> connected to every other neighbour of v). Let Cv denote the fraction of
> these allowable edges that actually exist. Define C as the average of
> Cv over all v."
>
> And Watts's book "Small Worlds" has a very similar definition. Consider
> a node with 1 neighbour; Cv for that node is clearly ill-defined (as it
> involves a divide by 0). There are two approaches to take when
> calculating C in a network with n nodes:
>
> i)add up Cv for all nodes where Cv is defined, and divide by n
> ii)add up Cv for all nodes where Cv is defined, and divide by the
> number of nodes for which Cv was defined
>
> i) seems to me to be the "obvious" interpretation of Watt's definition,
> but has the property that a large number of nodes of degree 1 will
> cause C to be small.
>
> I'd be interested to know what others think about this (or indeed to be
> pointed at a publication that discusses the two approaches).
>
> Thanks,
>
> Matthew
>
> [1] nature 393:440-442,1998
> --
> Matthew Vernon MA VetMB LGSM MRCVS
> Farm Animal Epidemiology and Informatics Unit
> Department of Veterinary Medicine, University of Cambridge
>
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