Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs

A. J. E. M. Janssen, Johan S. H. van Leeuwaarden, Seva Shneer

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
42 Downloads (Pure)


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 languageEnglish
Pages (from-to)161-184
Number of pages24
JournalJournal of Statistical Physics
Issue number1
Early online date18 Feb 2019
Publication statusPublished - Apr 2019


  • Cliques
  • Power-law distributions
  • Random graphs
  • Scale-free networks
  • Subgraphs

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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