Асимптротика числа ребер Интернет-графа

We consider configuration graphs with N vertices. The degrees of the vertices are independent and identically distributed according to a distribution law that depends on an unknown slowly varying function. The degree of a vertex has a finite expectation and an infinite variance. Such models can be used to describe various communication networks and Internet topologies. The paper proves the local limit theorem for the number of edges in a graph as N → ∞.