Dynamic community detection concerns inferring how community memberships evolve over time, including the emergence, persistence, merging, and dissolution of groups in temporal networks. We propose a Bayesian nonparametric model for time-evolving sparse networks, which captures power-law degree distributions and dynamically overlapping communities. The model is constructed from vectors of completely random measures coupled through a latent Markov process governing the evolution of 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 establish asymptotic results characterizing sparsity and degree heterogeneity over time, and develop an approximate inference procedure for recovering time-varying community trajectories. Applications to synthetic and real-world dynamic networks show that the model accurately uncovers evolving community structure and yields interpretable temporal patterns.

翻译：动态社区检测关注社区成员随时间演化的推断，包括时间网络中群体的出现、持续、合并与解散。我们提出一种针对时变稀疏网络的贝叶斯非参数模型，该模型能够捕获幂律度分布与动态重叠社区。模型通过完全随机测度向量构建，这些向量通过潜在马尔可夫过程耦合以控制节点归属的演化。该构建为建模动态社区提供了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与无标度情景。我们建立了刻画时变稀疏性与度异质性的渐近理论结果，并开发了近似推断流程以恢复时变社区轨迹。在合成与真实动态网络上的应用表明，该模型能够准确揭示演化的社区结构，并生成可解释的时间模式。