2023/12/05 by Mingao Yuan, Yuan, Mingao · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2312.03142
openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many real-world networks exhibit the phenomenon of edge clustering, which is typically measured by the average clustering coefficient. Recently, an alternative measure, the average closure coefficient, is proposed to quantify local clustering. It is shown that the average closure coefficient possesses a number of useful properties and can capture complementary information missed by the classical average clustering coefficient. In this paper, we study the asymptotic distribution of the average closure coefficient of a heterogeneous Erdös-Rényi random graph. We prove that the standardized average closure coefficient converges in distribution to the standard normal distribution. In the Erdös-Rényi random graph, the variance of the average closure coefficient exhibits the same phase transition phenomenon as the average clustering coefficient.