Scale-free network clustering in hyperbolic and other random graphs

Clara Stegehuis (Corresponding author), Remco van der Hofstad, Johan S.H. van Leeuwaarden

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)
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Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as resilience, navigability and small distances. We introduce a variational principle to explain how vertices tend to cluster in triangles as a function of their degrees. We apply the variational principle to the hyperbolic model that quickly gains popularity as a model for scale-free networks with latent geometries and clustering. We show that clustering in the hyperbolic model is non-vanishing and self-averaging, so that a single random graph sample is a good representation in the large-network limit. We also demonstrate the variational principle for some classical random graphs including the preferential attachment model and the configuration model.

Original languageEnglish
Article number295101
Number of pages20
JournalJournal of Physics A: Mathematical and Theoretical
Issue number29
Publication statusPublished - 24 Jun 2019


  • clustering
  • Complex networks
  • hyperbolic model
  • random graphs
  • complex networks


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