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Degree correlations in scale-free random graph models

Part of: Limit theorems Graph theory

Published online by Cambridge University Press:  01 October 2019

Clara Stegehuis
Clara Stegehuis*
Affiliation:
Eindhoven University of Technology
*
*Current address: Twente University, The Netherlands. Email address: c.stegehuis@utwente.nl
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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 $n^{(\tau-2)/(\tau-1)}$ and then settles on a power law $a(k)\sim k^{\tau-3}$, with $\tau$ the degree exponent.

Keywords

Degree correlationsrandom graph

MSC classification

Primary: 05C80: Random graphs
Secondary: 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 3 , September 2019 , pp. 672 - 700
Copyright
© Applied Probability Trust 2019 

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