Community detection in graphs can be viewed as the estimation of a partition map that remains stable under admissible perturbations of graph topology and node attributes. While modern graph neural networks (GNNs) achieve strong empirical accuracy, they often exhibit severe assignment drift under minor perturbations, leading to illusory community structures. In this work, we propose DISPEL-GNN, a stability-aware graph learning framework that integrates spectral operator regularization, Bayesian uncertainty modeling, and risk-aware dynamic attention for perturbation-bounded community detection. The model explicitly constrains graph operators through uniform spectral norm bounds, high-frequency energy suppression, and commutator alignment while dynamically modulating message passing based on node-level spectral risk and epistemic uncertainty. We further formalize instability via assignment of drift functional and establish perturbation bounds linking drift to operator norms and spectral gaps, complemented by a PAC-Bayesian generalization guarantee. Extensive experiments on real-world benchmarks including Cora, Citeseer, Pubmed, Cora-Full, and DBLP demonstrate that DISPEL-GNN consistently reduces assignment drift by 18–35% under feature noise and edge perturbations while improving clustering quality with up to +3.0 NMI and +0.04 ARI compared to strong baselines such as GAT and Bayesian GNNs. The normalized mutual information (NMI), adjusted Rand index (ARI), and PAC-Bayesian (PAC) constraints serve as evaluative and theoretical instruments in this study. Additional studies on synthetic graphs with controlled spectral gaps confirm that the proposed method maintains stable community assignments in low-gap regimes where classical spectral and GNN-based methods degrade sharply. These results establish DISPEL-GNN as a mathematically grounded and practically effective framework for robust and interpretable community detection. A metric-wise dominance analysis shows that DISPEL-GNN achieves metric-wise dominance across most accuracy and robustness criteria, with minor tradeoffs in modularity on selected datasets. These results indicate that explicitly modeling stability and uncertainty provides a principled pathway toward reliable and interpretable community detection in noisy graph environments.
Qu et al. (Mon,) studied this question.