PEANUT: Perturbations by Eigenvector Alignment for Attacking Graph Neural Networks Under Topology-Driven Message Passing

Message Passing Neural Networks (MPNNs) have achieved strong performance on tasks involving relational data. However, small perturbations to graph structure can significantly alter their outputs, raising concerns about their robustness in real-world deployment in security critical environments. In this work, we study a core vulnerability in MPNNs that explicitly consume graph topology via the adjacency matrix or Laplacian as part of their message passing mechanism. We show that this design choice exposes an extremely vulnerable attack surface, with significant effects even under minimal perturbation. Building on this observation, we propose PEA, a simple, gradient-free, black-box injection attack that requires only a single query to the target model, capitalizing on this vulnerability by constructing a perturbation aligned with a specific significant eigenvector to induce large output deviations. Unlike graph modification attacks, PEA operates under the realistic assumption that adversaries cannot alter the original graph and are limited to injecting new nodes at inference time. PEA requires no iterative optimization, parameter learning, or surrogate models---which require additional training and remain susceptible to differences in model priors and generalization capabilities---thereby avoiding significant computational overhead and the associated transferability challenges. We evaluate PEA on popular benchmark datasets across three graph learning tasks, showing consistent performance degradation under realistic attack constraints despite its simplicity. Our results reveal a fundamental security weakness in topology-driven message passing architectures and urge an implementation shift, as the worst effects of such attacks can be substantially mitigated through appropriate input filtering.