Counting cliques and cycles in scale-free inhomogeneous random graphs

A.J.E.M. Janssen, Johan S.H. van Leeuwaarden (Corresponding author), Seva Shneer

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    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 Jan 2019
    Publication statusPublished - 15 Apr 2019


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

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