Scientific publications

We study random graphs consisting of N numbered vertices. 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. Recent studies show that such random graphs can be used for modeling the Internet topology. We obtain the limit distribution of the maximum vertex degree under the condition that the sum of vertex degrees is equal to n, n is even, τ<1 and N, n →∞ such that n/N1/τ →∞.