SFB-GNN: Perturbation-Stable Community Detection with Self-Regulating Fourier–Bayesian Graph Neural Networks

Community detection in attributed graphs can be highly unstable under small structural or feature perturbations, causing large changes in inferred partitions even when the underlying community structure remains largely unchanged. We introduce SFB-GNN, a self-regulating Fourier–Bayesian graph neural network designed to directly control this perturbation-induced assignment drift. SFB-GNN combines bounded polynomial spectral filtering, Bayesian epistemic uncertainty estimation, and uncertainty-aware adaptive message gating within a closed-loop stability framework. The spectral component limits perturbation amplification during graph propagation, while uncertainty estimates identify structurally vulnerable regions and selectively regulate message passing. To directly stabilize community assignments, we further introduce a permutation-invariant co-assignment consistency objective between clean and perturbed graph views. Experiments on real-world attributed graphs and synthetic graphs with controlled spectral gaps show that SFB-GNN substantially reduces assignment drift under structural and feature perturbations while preserving competitive clustering quality. Ablation and sensitivity analyses confirm that spectral regulation, uncertainty estimation, and adaptive gating provide complementary contributions to stability without inducing representation collapse. These results show that explicitly regulating perturbation propagation and assignment consistency provides an effective approach to reliable community detection under noisy and uncertain graph observations.