Degree correlations in scale-free random graph models

Clara Stegehuis*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study the average nearest-neighbour degree a(k) of vertices with degree k. In many real-world networks with power-law degree distribution, a(k) falls off with k, a property ascribed to the constraint that any two vertices are connected by at most one edge. We show that a(k) indeed decays with k in three simple random graph models with power-law degrees: the erased configuration model, the rank-1 inhomogeneous random graph, and the hyperbolic random graph. We find that in the large-network limit for all three null models, a(k) starts to decay beyond and then settles on a power law , with the degree exponent.

Original languageEnglish
Pages (from-to)672-700
Number of pages29
JournalJournal of applied probability
Volume56
Issue number3
DOIs
Publication statusPublished - 1 Sep 2019
Externally publishedYes

Keywords

  • Degree correlations
  • random graph

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