Dynamic community detection in networks addresses the challenge of tracking how groups of interconnected nodes evolve, merge, and dissolve within time-evolving networks. Here, we propose a novel statistical framework for sparse networks with power-law degree distribution and dynamic overlapping community structure. Using a Bayesian Nonparametric framework, we build on the idea to represent the graph as an exchangeable point process on the plane. We base the model construction on vectors of completely random measures and a latent Markov process for the time-evolving node affiliations. This construction provides a flexible and interpretable approach to model dynamic communities, naturally generalizing existing overlapping block models to the sparse and scale-free regimes. We provide the asymptotic properties of the model concerning sparsity and power-law behavior and propose inference through an approximate procedure which we validate empirically. We show how the model can uncover interpretable community trajectories in a real-world network.

翻译：网络中的动态社区检测旨在解决跟踪时间演化网络中相互连接节点群的演变、合并与解体的挑战。本文提出了一种针对具有幂律度分布和动态重叠社区结构的稀疏网络的新型统计框架。基于贝叶斯非参数框架，我们采用将图表示为平面上可交换点过程的思想。模型构建基于完全随机测度向量和用于时间演化节点归属的隐马尔可夫过程。该构建为建模动态社区提供了一种灵活且可解释的方法，自然地将现有重叠块模型推广至稀疏和无标度体系。我们给出了模型在稀疏性和幂律行为方面的渐近性质，并提出了一种经验验证的近似推断方法。我们展示了该模型如何在真实世界网络中揭示可解释的社区演化轨迹。