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.Comment: 21 pages, 4 figure