Ю.Л. Павлов.
О типичной структуре конфигурационного интернет-графа с известным числом связей
// Труды КарНЦ РАН. No 5. Сер. Математическое моделирование и информационные технологии, вып. 2. 2011. C. 86-96
Yu.L. Pavlov. On the typical structure of configuration internet graph with known number of links // Transactions of Karelian Research Centre of Russian Academy of Science. No 5. Mathematical Modeling and Information Technologies. 2011. Pp. 86-96
Keywords: random graph, Internet, configuration model, random structure.
We consider the configuration model of random graph consisting of N vertices. The degrees of vertices are drawn independently from power-law distribution with the exponent τ ∈ (1; 2) under the condition that the sum of vertex degree is equal to n. We show that if N; n → ∞ in such a way that n ζ( τ )N = O(N1/τ), where ζ(x) is the Rimann‘s zeta-function, then the limit structure of the graph is the same typical structure as the random graph without the condition on the sum of degrees.
