Targeted attack in spatial networks with minimal collateral damage

Targeted attacks in spatial networks have a wide range of applications in real systems such as transportation, power grids, and communication networks, but they may cause collateral damage in systems, so how to develop targeted attacks is an important research problem. This study introduces the reverse gradient attack (RGA), a novel efficient strategy designed to optimize attack precision while minimizing collateral damage. By incorporating spatial constraints and leveraging a gradient-based intensity mapping framework, RGA identifies the optimal attack centers for precise targeted interventions. A comprehensive evaluation across multiple real-world spatial networks demonstrates that RGA outperforms traditional methods in terms of precision and robustness, particularly in scenarios requiring minimal influence to non-target nodes. The study highlights a “black zone” phenomenon, referring to regions where increasing the attack radius paradoxically reduces the effectiveness of the attack, further highlighting the importance of carefully selecting the attack radius. The findings reveal RGA’s effectiveness in both random and topologically clustered target scenarios, suggesting the robustness of the methodology of targeted attacks in spatial networks.