Triadic closure in configuration models with unbounded degree fluctuations

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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=Ω(n − − √ ) settles on a power law c(k)∼k −2(3−τ) with τ∈(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.
Originele taal-2Engels
Artikelnummer1710.02027v1
Aantal pagina's25
TijdschriftarXiv
Nummer van het tijdschrift1710.02027
StatusGepubliceerd - 5 okt 2017

Trefwoorden

  • math.PR

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