H-MGC: Multi-Scale Graph Clustering through Adaptive Motif Resolution Fusion

Graph clustering is a fundamental task in network analysis with wide applications in social networks, bioinformatics, and knowledge graphs. Traditional clustering methods primarily rely on low-order connectivity patterns, often overlooking the rich structural information encoded in higher-order motifs. To address this limitation, we propose H-MGC, a novel multi-motif multi-resolution graph clustering framework that systematically integrates heterogeneous structural information across different scales. The key innovation of H-MGC lies in its dual adaptive learning mechanism: at the inter-layer level, it automatically learns the importance weights of different motif-resolution combinations through entropy-regularized optimization; at the intra-layer level, it incorporates node-specific gating factors to capture local structural heterogeneity. Our method employs an alternating optimization strategy that efficiently solves the unified objective function through spectral embedding, weight updating, and gating learning. Comprehensive experiments on five real-world and synthetic datasets demonstrate that H-MGC consistently outperforms baselines across multiple evaluation metrics. On the Cora dataset, H-MGC achieves improvements of 8.6%, 7.4%, and 5.4% in accuracy compared to baseline, while maintaining reasonable computational efficiency. Further analysis reveals that our adaptive fusion strategy effectively captures both local and global structural patterns, with triangle motifs emerging as the most significant structural feature in citation networks. The convergence and efficiency analysis confirms the stability and practicality of our approach for large-scale network analysis.