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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Published in | Acta mathematica Hungarica Vol. 172; no. 2; pp. 543 - 569 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.04.2024
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0236-5294 1588-2632 |
DOI: | 10.1007/s10474-024-01416-z |