The structure of complex networks is an important aspect in the study of the real network data. Quite often, it is desirable to know the division of the network into communities. A large number of community detection algorithms have been proposed to probe the community structure of complex networks. For a specific partition of a given network, we show that the distribution of modularity under a null hypothesis of free labeling is asymptotically normal when the size of the network gets large. The significance of the partition is defined based on this asymptotic distribution, which can help assess its goodness. Two different partitions can also be compared statistically. Simulation studies and real data analyses are performed for illustration.

中文翻译：

---

网络中模块化的渐近分布

复杂网络的结构是研究真实网络数据的一个重要方面。很多时候，需要知道将网络划分为社区。已经提出了大量的社区检测算法来探测复杂网络的社区结构。对于给定网络的特定分区，我们表明，当网络规模变大时，自由标记零假设下的模块化分布是渐近正态的。分区的重要性是根据这种渐近分布来定义的，这有助于评估其优劣。两个不同的分区也可以进行统计比较。进行模拟研究和实际数据分析以进行说明。