Ю.Л. Павлов.
О предельных распределениях степеней вершин условного конфигурационного случайного графа
// Труды КарНЦ РАН. No 5. Сер. Математическое моделирование и информационные технологии. Вып. 3. 2012. C. 78-88
Yu.L. Pavlov. On limit distributions of vertex degrees in conditional configuration random graph // Transactions of Karelian Research Centre of Russian Academy of Science. No 5. Mathematical Modeling and Information Technologies. Vol. 3. 2012. Pp. 78-88
Keywords: random graphs, Internet, configuration model, vertex degree, limit distribution
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)/N1/τ → ∞.
