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.

翻译：全局聚类系数是分析和比较复杂网络结构的有效度量。随机环图是著名的Erd\H{o}s-R\'{e}nyi随机图的一种改进形式，最近被提出用于网络社区建模。本文研究了随机环图中全局聚类系数的渐近分布。研究表明，标准化的全局聚类系数依分布收敛于标准正态分布。该结果通过使用具有样本量依赖核的退化U-统计量渐近理论得以建立。据我们所知，该方法不同于推导网络统计量渐近分布的现有方法。此外，我们得到了全局聚类系数极限的显式表达式。