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Павлов Ю.Л.
О локальном кластерном коэффициенте конфигурационного графа
// Труды КарНЦ РАН. No 4. Сер. Математическое моделирование и информационные технологии. 2025. C. 44-53
Pavlov Yu.L. On the local clustering coefficient of a configuration graph // Transactions of Karelian Research Centre of Russian Academy of Science. No 4. Mathematical Modeling and Information Technologies. 2025. Pp. 44-53
Keywords: configuration graph; local clustering coefficient; limit theorems
We consider configuration graphs with N vertices whose degrees are independent
and identically distributed. The distribution of the random variable ξ, which is
defined as the degree of any vertex, is assumed to satisfy the condition
P{ξ = k} ∼ L / (kτ lng k),
as k→∞, where L, g > 0, τ ∈ (2, 3). We study the local clustering coefficient c(s) which can be interpreted as the probability that two different vertices adjacent to
a vertex of degree s are also connected by an edge. The limit theorem is proved for
the c(s) as N →∞ and s = o(N(τ−2)/(τ−1)).
and identically distributed. The distribution of the random variable ξ, which is
defined as the degree of any vertex, is assumed to satisfy the condition
P{ξ = k} ∼ L / (kτ lng k),
as k→∞, where L, g > 0, τ ∈ (2, 3). We study the local clustering coefficient c(s) which can be interpreted as the probability that two different vertices adjacent to
a vertex of degree s are also connected by an edge. The limit theorem is proved for
the c(s) as N →∞ and s = o(N(τ−2)/(τ−1)).
DOI: 10.17076/mat2024
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Last modified: June 28, 2025