SOCNET@LISTS.UFL.EDU

View:

 Message: [ First | Previous | Next | Last ] By Topic: [ First | Previous | Next | Last ] By Author: [ First | Previous | Next | Last ] Font: Monospaced Font

Subject:

clustering coefficient edge-case

From:

Date:

Wed, 12 Jan 2005 15:44:54 +0000

Content-Type:

text/plain

Parts/Attachments:

 text/plain (44 lines)
 ***** 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 _____________________________________________________________________ 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.