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.
- Power-law distributions
- Random graphs
- Scale-free networks
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Janssen, A. J. E. M., van Leeuwaarden, J. S. H., & Shneer, S. (2019). Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs. Journal of Statistical Physics, 175(1), 161-184. https://doi.org/10.1007/s10955-019-02248-w