Scale-free network clustering in hyperbolic and other random graphs

Clara Stegehuis, Remco van der Hofstad, Johan S. H. van Leeuwaarden

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Abstract

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
JournalJournal of physics A: mathematical and theoretical
Volume52
Issue number29
Early online date17 May 2019
DOIs
Publication statusPublished - 24 Jun 2019
Externally publishedYes

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Keywords

  • physics.soc-ph
  • cs.SI
  • math.PR

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