О распределении вторых степеней вершин конфигурационных графов
Keywords: configuration graph; second degree of vertex; generating function; limit distribution
The object is configuration graphs with N vertices, numbered from 1 to N, whose vertex degrees are independent identically distributed random variables. The second degree η(2) of an arbitrary vertex A of a configuration graph is equal to the sum of the degrees of the vertices adjacent to the vertex A excluding the edges going to A. As N →∞, the form of the generating function and the distribution of the random variable η(2) are found for graphs whose vertex degrees have the Poisson distribution. Also, as N →∞, the form of the generating function of a random variable η(2) is obtained for graphs with the vertex degree distribution pk > 0, k= 1, 2, ..., such that pk ∼ d/kg( lnk)h, h 0, g>7/3, d>0, as k→∞.
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