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Re: clustering coefficient edge-case

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Wed, 12 Jan 2005 16:38:18 -0500

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 ```***** To join INSNA, visit http://www.insna.org ***** My read on C(1) and C(2) is that they are not probabilities     at all (at least I don't see a probabilistic model in use     in this part of Mark's paper) but are simply triad counts. As such, there are MANY different kinds/types/varieties of     triad counts (for different types of relations) --- Steven,     let me suggest you consult the literature on transitivity     and clusterability (which is extensive, and generated many     different kinds of "clustering coefficient"). Stan Wasserman ************ On Jan 12, 2005, at 11:32 AM, Mark Newman wrote: On Wednesday 12 January 2005 11:18 am, Steven L. Johnson wrote: ***** To join INSNA, visit http://www.insna.org ***** 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?? **************** Both definitions can be described in words simply enough. C(1) is "the probability that two people with a common acquaintance know one another". (There's some subtleties about that, but that's the basic idea.) C(2) is "the probability that two acquaintances of a randomly chosen person know each other". Thus the crucial difference is whether you are focusing on the two people or on their common acquaintance. One can imagine experimental designs in which either of these two definitions might be useful. Where mathematical calculations are concerned, however, the first is almost invariably easier to calculate. Mark Newman ************************************* Stanley Wasserman Sociology and Psychology Indiana University [log in to unmask] http://www.indiana.edu/~appstat/ ************************************* _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.```