Triadic closure in configuration models with unbounded degree fluctuations

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

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6 Citations (Scopus)
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Abstract

The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded degree fluctuations. For this setting, we study the local clustering $c(k)$, i.e., the probability that two neighbors of a degree-$k$ node are neighbors themselves. We show that $ c(k)$ progressively falls off with $k$ and eventually for $k=\Omega(\sqrt{n})$ settles on a power law $c(k)\sim k^{-2(3-\tau)}$ with $\tau\in(2,3)$ the power-law exponent of the degree distribution. This fall-off has been observed in the majority of real-world networks and signals the presence of modular or hierarchical structure. Our results agree with recent results for the hidden-variable model and also give the expected number of triangles in the configuration model when counting triangles only once despite the presence of multi-edges. We show that only triangles consisting of triplets with uniquely specified degrees contribute to the triangle counting.
Original languageEnglish
Pages (from-to)746-774
JournalJournal of statistical physics
Volume173
Issue number3-4
Early online date25 Jan 2018
DOIs
Publication statusPublished - 1 Nov 2018
Externally publishedYes

Keywords

  • math.PR

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