Community structure in networks naturally arises in various applications. But while the topic has received significant attention for static networks, the literature on community structure in temporally evolving networks is more scarce. In particular, there are currently no statistical methods available to test for the presence of community structure in a sequence of networks evolving over time. In this work, we propose a simple yet powerful test using e-values, an alternative to p-values that is more flexible in certain ways. Specifically, an e-value framework retains valid testing properties even after combining dependent information, a relevant feature in the context of testing temporal networks. We apply the proposed test to synthetic and real-world networks, demonstrating various features inherited from the e-value formulation and exposing some of the inherent difficulties of testing on temporal networks.

翻译：网络中的社区结构在各种应用中自然产生。然而，尽管静态网络的社区结构研究已获得广泛关注，关于时序演化网络中社区结构的文献则相对稀缺。特别是，目前尚缺乏统计方法来检验随时间演化的网络序列中是否存在社区结构。本研究提出了一种基于e值的简单而有效的检验方法，e值是p值的一种替代方案，在某些方面更具灵活性。具体而言，e值框架即使在整合依赖信息后仍能保持有效的检验特性，这一特征在时序网络检验中尤为重要。我们将所提出的检验方法应用于合成网络和真实网络，展示了e值框架所继承的多种特性，并揭示了时序网络检验中固有的一些难点。