Scientific publications

We study random graphs consisting of N numbered verties. The degrees of the vertices are drawn independently from power-law distribution with the exponent τ > 0. All of the stubs of the vertices are numbered. The graph is constructed by joining each stub to another equiprobably to form edges. We obtain the limit distributions of the maximum vertex degree and number of vertices with given degree under the condition that the sum of vertex degrees is equal to n; n is even, τ ∈ (1; 2) and N; n → ∞ so that (n − ζ(τ)N)/N^1/τ → ∞.