Overlapping Community Detection and Evolution Analysis in Temporal Hypergraphs

Higher-order interactions, overlapping memberships, and structural evolution frequently co-occur in complex systems. Temporal hypergraphs can naturally capture such scenarios. This paper focuses on the evolution analysis of overlapping communities in temporal hypergraphs. It builds upon a static generative model and incorporates temporal smoothing. The method assigns each node a time-varying mixed membership vector. It also assigns a community relationship matrix to each time slice. As a result, observed hyperedges can be explained by node-level engagement and interaction patterns among communities. To maintain the continuity of the evolutionary process, the method incorporates several strategies. These include temporal smoothing, warm-start inference, community alignment, and state fusion. These strategies help distinguish genuine structural changes from local fluctuations. This paper evaluates the learned representations through three types of tasks: real-world data analysis, controlled synthetic scenarios, and link prediction. The results demonstrate that the proposed method can recover fluctuations in community size across different stages. It can also identify transitions between intra-community cohesion and inter-community coupling. Moreover, it reveals the step-by-step migration trajectories of representative nodes. Compared to dynamic graph baseline models, the temporal community representation learned in this study performs comparably. This framework provides an interpretable and practical tool for analyzing the evolution of mesoscale organization in temporal hypergraphs.