Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks

Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering. While low-order spectral filters are efficient, their limited selectivity often leads to weak attenuation outside the passband, whereas high-order alternatives introduce optimization challenges. We propose DCQ-GNN, a spectral GNN based on a compact bank of adaptive convex--concave quadratic filters. By restricting the filter order to two while explicitly exploiting complementary curvature, DCQ-GNN improves spectral selectivity as quantified by Dirichlet energy and entropy measures without resorting to high-order polynomial expansions. The model fuses filter outputs through a node-adaptive gating mechanism to enable node-wise structure-aware spectral selection. We provide a formal spectral analysis grounded in Dirichlet energy attenuation, von Neumann entropy, and curvature polarity, and derive explicit characterizations of filter behavior across varying levels of homophily and structural perturbations. Extensive benchmarks on 10 datasets show that DCQ-GNN ties for the top average rank (3.0) on heterophilic graphs and obtains the second-best rank (4.2) on homophilic graphs, remaining competitive with representative high-order polynomial spectral filters. Furthermore, under strong structural perturbations, DCQ-GNN exhibits substantially smaller performance degradation compared to both first-order and high-order baselines. These results demonstrate that curvature-aware quadratic banks provide a robust and efficient alternative to high-order spectral models while preserving optimization stability and computational efficiency.

Single-Edge Node Injection Threats to GNN-Based Security Monitoring in Industrial Graph Systems

Graph neural networks (GNNs) are increasingly adopted in industrial graph-based monitoring systems (e.g., Industrial internet of things (IIoT) device graphs, power-grid topology models, and manufacturing communication networks) to support anomaly detection, state estimation, and asset classification. In such settings, an adversary that compromises a small number of edge devices may inject counterfeit nodes (e.g., rogue sensors, virtualized endpoints, or spoofed substations) to bias downstream decisions while evading topology- and homophily-based sanitization. This paper formulates deployment-oriented node-injection attacks under constrained resources and proposes the \emph{Single-Edge Graph Injection Attack} (SEGIA), in which each injected node attaches to the operational graph through a single edge. SEGIA integrates a pruned SGC surrogate, multi-hop neighborhood sampling, and reverse graph convolution-based feature synthesis with a similarity-regularized objective to preserve local homophily and survive edge pruning. Theoretical analysis and extensive evaluations across datasets and defenses show at least $25\%$ higher attack success than representative baselines under substantially smaller edge budgets. These results indicate a system-level risk in industrial GNN deployments and motivate lightweight admission validation and neighborhood-consistency monitoring.