The Clustering Coefficient of a Scale-Free Random Graph

Eggemann, Nicole
Noble, Steven D.
Description
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.
Comment: 17 pages. Submitted
Keywords
Mathematics - Combinatorics, 05C80 (Primary) 68R10, 60C05 (Secondary)