Clique and cycle frequencies in a sparse random graph model with overlapping communities

Tommi Gröhn, Joona Karjalainen*, Lasse Leskelä

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


Abstract.: A statistical network model with overlapping communities can be generated as a superposition of mutually independent random graphs of varying size. The model is parameterized by the number of nodes, the number of communities, and the joint distribution of the community size and the edge probability. This model admits sparse parameter regimes with power-law limiting degree distributions and non-vanishing clustering coefficients. This article presents large-scale approximations of clique and cycle frequencies for graph samples generated by the model, which are valid for regimes with unbounded numbers of overlapping communities. Our results reveal the growth rates of these subgraph frequencies and show that their theoretical densities can be reliably estimated from the data.

Original languageEnglish
JournalStochastic models
Publication statusE-pub ahead of print - 2024
MoE publication typeA1 Journal article-refereed


  • Network motif
  • overlapping communities
  • statistical network model


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