Scale-free network clustering in hyperbolic and other random graphs

Clara Stegehuis*, Remco van Der Hofstad, Johan S. H. van Leeuwaarden

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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
DOIs
Publication statusPublished - 19 Jul 2019

Keywords

  • complex networks
  • random graphs
  • hyperbolic model
  • clustering
  • COMPLEX NETWORKS
  • ORGANIZATION
  • DISTANCES
  • WEB
  • DIAMETER
  • INTERNET
  • MODELS

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