Scale-free network clustering in hyperbolic and other random graphs

Clara Stegehuis (Corresponding author), 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
Number of pages20
JournalJournal of Physics A: Mathematical and Theoretical
Volume52
Issue number29
DOIs
Publication statusPublished - 24 Jun 2019

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Scale-free Networks
Complex networks
Random Graphs
Clustering
variational principles
Variational Principle
resilience
Model
applications of mathematics
scale models
Preferential Attachment
triangles
Resilience
attachment
Mathematical Analysis
apexes
topology
Averaging
Triangle
Power Law

Keywords

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

Cite this

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Scale-free network clustering in hyperbolic and other random graphs. / Stegehuis, Clara (Corresponding author); van der Hofstad, Remco; van Leeuwaarden, Johan S.H.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 52, No. 29, 295101, 24.06.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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