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.
Original language | English |
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Pages (from-to) | 161-184 |
Number of pages | 24 |
Journal | Journal of Statistical Physics |
Volume | 175 |
Issue number | 1 |
Early online date | 18 Jan 2019 |
DOIs | |
Publication status | Published - 15 Apr 2019 |
Keywords
- Cliques
- Power-law distributions
- Random graphs
- Scale-free networks
- Subgraphs