Central limit theorem for the average closure coefficient

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...

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Bibliographic Details
Published inActa mathematica Hungarica Vol. 172; no. 2; pp. 543 - 569
Main Author Yuan, M.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2024
Springer Nature B.V
Subjects
Clustering
Coefficients
Mathematics
Mathematics and Statistics
Normal distribution
Phase transitions
asymptotic distribution
average closure coefficient
random graph
phase transition
05C80
60K35
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Summary: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 Erdős–Rényi random graph. We prove that the standardized average closure coefficient converges in distribution to the standard normal distribution. In the Erdős–Rényi random graph,the variance of the average closure coefficient exhibits the same phase transition phenomenon as the average clustering coefficient.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-024-01416-z