Counting cliques and cycles in scale-free inhomogeneous random graphs
Probability
2019-03-27 v1
Abstract
Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral expressions amenable to asymptotic analysis. We obtain various asymptotic descriptions for how the average number of cliques and cycles, of any size, grow with the network size. For the cycle asymptotics we invoke the theory of circulant matrices.
Cite
@article{arxiv.1812.04384,
title = {Counting cliques and cycles in scale-free inhomogeneous random graphs},
author = {A. J. E. M. Janssen and Johan S. H. van Leeuwaarden and Seva Shneer},
journal= {arXiv preprint arXiv:1812.04384},
year = {2019}
}