The classification of different patterns of network evolution, for example in brain connectomes or social networks, is a key problem in network inference and modern data science. Building on the notion of a network's Euclidean mirror, which captures its evolution as a curve in Euclidean space, we develop the Dynamic Network Clustering through Mirror Distance (DNCMD), an algorithm for clustering dynamic networks based on a distance measure between their associated mirrors. We provide theoretical guarantees for DNCMD to achieve exact recovery of distinct evolutionary patterns for latent position random networks both when underlying vertex features change deterministically and when they follow a stochastic process. We validate our theoretical results through numerical simulations and demonstrate the application of DNCMD to understand edge functions in Drosophila larval connectome data, as well as to analyze temporal patterns in dynamic trade networks.

翻译：对网络演化不同模式的分类（例如在脑连接组或社交网络中）是网络推断和现代数据科学中的一个关键问题。基于网络的欧几里得镜像概念——该概念将网络演化捕获为欧几里得空间中的一条曲线——我们开发了通过镜像距离进行动态网络聚类（DNCMD）算法，该算法基于其关联镜像之间的距离度量对动态网络进行聚类。我们为DNCMD提供了理论保证，使其能够在底层顶点特征确定性变化以及遵循随机过程时，对潜在位置随机网络的不同演化模式实现精确恢复。我们通过数值模拟验证了我们的理论结果，并展示了DNCMD在理解果蝇幼虫连接组数据中的边缘功能，以及分析动态贸易网络中的时间模式方面的应用。