The configuration graph where vertex degrees are independent identically distributed random variables is often used for models of complex networks such as the Internet. We consider a random graph consisting of N+1 vertices. The random variables η1,…,ηN are equal to the degrees of vertices with the numbers 1,… ,N. The probability P{ηi=k}, i=1,…, N, is equivalent to h(k)/kτ as k→∞ where h(x) is a slowly varying function integrable in any finite interval, τ>1. The vertex 0 has degree 0 if the sum of degrees of all other vertices is even, else the degree is 1. We obtain the limit distribution of the maximum vertex degree and the number of vertices with a given degree under the condition that the sum of degrees is equal to n and N,n→∞, 1

URL: http://journals.krc.karelia.ru/index.php/mathem/article/view/138

DOI: 10.17076/mat138

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