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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(Οβ2)/(Οβ1) and then settles on a power law a(k)βΌkΟβ3, with Ο the degree exponent
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