English

The Clustering Coefficient of a Scale-Free Random Graph

Combinatorics 2008-04-21 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0804.3032,
  title  = {The Clustering Coefficient of a Scale-Free Random Graph},
  author = {Nicole Eggemann and Steven D. Noble},
  journal= {arXiv preprint arXiv:0804.3032},
  year   = {2008}
}

Comments

17 pages. Submitted

R2 v1 2026-06-21T10:32:34.723Z