The Clustering Coefficient of a Scale-Free Random Graph

Details The Clustering Coefficient of a Scale-Free Random Graph The Clustering Coefficient of a Scale-Free Random Graph

2008-04-18

arxiv.org/abs/0804.3032v1

Mathematics

Combinatorics

17 pages. Submitted

Scientific paper

We consider a random graph process in which, at each time step, a new vertex is added with m out-neighbours, chosen with probabilities proportional to their degree plus a strictly positive constant. We show that the expectation of the clustering coefficient of the graph process is asymptotically proportional to log n/n. Bollob\'as and Riordan have previously shown that when the constant is zero, the same expectation is asymptotically proportional to ((log n)^2)/n.

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