О глобальном кластерном коэффициенте Интернет-графа
// Труды КарНЦ РАН. No 4. Сер. Математическое моделирование и информационные технологии. 2023. C. 50–53
Pavlov Yu.L. On the Internet-graph clustering coefficient // Transactions of Karelian Research Centre of Russian Academy of Science. No 4. Mathematical Modeling and Information Technologies. 2023. P. 50–53
Keywords: random configuration graph; clustering coefficient; limit theorem
We consider a configuration graph with N vertices whose degrees are independent and identically distributed according to the power law depending on a slowly varying function. Configuration graphs are widely used for modeling complex communication networks such as the Internet. The parameter of the power-law distribution is usually selected so that the vertex degree distribution has a finite expectation and infinite variance. An important characteristic of the topology of a configuration graph is the global clustering coefficient. Clustering measures the extent to which neighbours of vertices are also each other’s neighbours. We prove the limit theorem for the clustering coefficient as N tends to infinity.
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