TSA-HGNN: a stability-aware multi-scale temporal graph neural network for dynamic community detection

Dynamic community detection is an increasingly important research topic in network science. In real-world networks, edges and nodes change over time; therefore, the community structure must evolve. Due to the dynamic nature of networks, many community detection algorithms rely on static graph assumptions and may not perform well in dynamic networks. Furthermore, the community assignments between snapshot graphs may not be stable. In this study, we designed a stability-aware, multi-scale temporal graph neural network, TSA-HGNN, for dynamic community detection. The proposed TSA-HGNN framework comprises three main components. First, we utilized GraphSAGE to obtain the snapshot-level spatial embedding. Second, the GraphSAGE outputs are fed into two temporal components to model multi-scale temporal patterns in evolving graphs: a temporal convolutional network (TCN) for short-term patterns and an Informer with ProbSparse attention for long-term patterns. Third, we adopted an echo state network (ESN) as an auxiliary component. Moreover, we imposed an additional temporal smoothness constraint on the output community assignments to further enhance stability across consecutive snapshots. To facilitate stable training, we propose a joint optimization framework for TSA-HGNN. Experimental results on three main benchmark datasets (Community Detection Dataset, Reddit Hyperlink Network, and DBLP Collaboration Network), together with an additional temporal benchmark dataset for extended evaluation, validate the superior performance of TSA-HGNN compared with state-of-the-art algorithms DeepWalk, Node2Vec, TGN, TGAT, and GCN-LSTM. The accuracy values for these datasets are 0.9843, 0.9755, and 0.9931, respectively. The F-Score, Modularity Q, NMI, and ARI for TSA-HGNN are 0.9807, 0.8273, 0.8878, and 0.8677, respectively, and achieve state-of-the-art results. Furthermore, temporal stability is further supported by explicit community switch-rate analysis, and the reported improvements are reinforced by corrected statistical significance tests across the main evaluation metrics. Therefore, TSA-HGNN not only enables dynamic community detection more efficiently but also achieves highly stable results.