标题： 随机环形图中全局聚类系数的渐近分布 显示英文标题

标题： Asymptotic distribution of the global clustering coefficient in a random annulus graph

摘要： 全局聚类系数是分析和比较复杂网络结构的有效度量。 随机环形图是著名的Erdős-Rényi随机图的改进版本。 它最近被提出用于建模网络社区。 本文研究了随机环形图中全局聚类系数的渐近分布。 结果表明，标准化的全局聚类系数在法律上收敛到标准正态分布。 该结果是通过使用具有样本量依赖核的退化U统计量的渐近理论建立的。 据我们所知，这种方法与推导网络统计量渐近分布的现有方法不同。 此外，我们得到了全局聚类系数极限的显式表达式。 显示英文摘要

摘要： The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been recently proposed in modeling network communities. This paper investigates the asymptotic distribution of the global clustering coefficient in a random annulus graph. It is demonstrated that the standardized global clustering coefficient converges in law to the standard normal distribution. The result is established using the asymptotic theory of degenerate U-statistics with a sample-size dependent kernel. As far as we know, this method is different from established approaches for deriving asymptotic distributions of network statistics. Moreover, we get the explicit expression of the limit of the global clustering coefficient.