Degree correlations in scale-free null models

2017/09/04 by Stegehuis, Clara
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1709.01085

Abstract

We study the average nearest neighbor degree a(k) of vertices with degree k. In many real-world networks with power-law degree distribution a(k) falls off in 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 in k in three simple random graph null models with power-law degrees: the erased configuration model, the rank-1 inhomogeneous random graph and the hyperbolic random graph. We consider the large-network limit when the number of nodes n tends to infinity. We find for all three null models that a(k) starts to decay beyond n^{(τ-2)/(τ-1)} and then settles on a power law a(k)∼ k^τ-3, with τ the degree exponent.

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