EFB-GNN: Energy-Centric Spectral Fourier–Bayesian Control and Community Dynamics Detection in Graph Neural Network System

Community detection in attributed graphs is extremely sensitive to minor structural and feature perturbations, frequently resulting in sudden assignment alterations despite competitive clustering accuracy in pristine conditions. This illusory instability undermines the trustworthiness of graph learning models in real-world contexts where noise, dynamic evolution, and structural uncertainty are inevitable. In this study, we introduce EFB-GNN, an Energy-centric Fourier–Bayesian Graph Neural Network that explicitly incorporates spectral stability regulation, Bayesian uncertainty modeling, and community-aware message control into a cohesive framework. The model restricts the spectrum response of graph propagation operators by polynomial Fourier filtering, while variational Bayesian inference assesses epistemic uncertainty. Comprehensive experiments on various real-world graphs, ranging from weak to strong homophily, sparse to dense connectivity, and small to large scales, reveal that EFB-GNN consistently mitigates assignment drift amid both structural and feature perturbations while preserving competitive clustering accuracy. The sensitivity analysis within regulated spectral gap conditions verifies that the proposed framework attains significant stability improvements without causing representation collapse or undue smoothing. These findings confirm stability-aware community discovery as a systematic enhancement of graph representation learning, integrating spectral graph theory, probabilistic inference, and resilient graph modeling.