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Hi Gizem, all,

You *really* bump into these kinds of graphs when dealing with any social network?? :)
Let me guess, you do game theory, right? ;)
(ok, i confess i cheated)

--	Christophe.



Le 9 déc. 2010 à 20:47, Gizem Korkmaz a écrit :

> ***** To join INSNA, visit http://www.insna.org ***** Hi,
> 
> I wanted to ask a quick question on graph theory.. I'd be very thankful if you could help me with it..
> 
> A k-regular simple graph G on v nodes is strongly k-regular if there exist positive integers (k,s,m) such that every vertex has k neighbors (i.e., the graph is regular),  every adjacent pair of vertices has 's' common neighbors, and every nonadjacent pair has 'm' common neighbors (West 2000, pp. 464-465).
> 
> I am looking for graphs for which the last property (that every nonadjacent pair has m common neighbors) is relaxed. So, the nonadjacent pairs might have different number of common neighbours, while adjacent pairs have same number of common neighbors. (a cycle graph with n>5 is an example of such a graph). Do you know whether this family of graphs have a particular name in the literature so that I can check for their properties?
> 
> Thank you very much in advance!
> 
> best,
> 
> Gizem Korkmaz
> European University Institute
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