Examining vulnerability of planar networks from a large-scale region segmentation perspective.

Evaluating the vulnerability of planar networks, such as road systems, is crucial for optimizing network topology and enhancing network defensive capabilities. In this study, we introduce the concept of "large-scale region segmentation" and propose a novel approach for assessing the vulnerability of planar networks. To validate our method, we employ the network efficiency metric to quantify network performance under various attack scenarios, with taking random failures and betweenness-based targeted attacks for comparison. Experiments are conducted on both real-world urban road networks (including Atlanta, Chengdu, Florence, and Paris) and randomly generated planar networks. Results across all tested datasets indicate that the proposed method outperforms both random and betweenness-based attack strategies in rapidly degrading network efficiency. The main contribution of this work lies in considering the overall connectivity of planar networks, rather than focusing solely on individual nodes or edges, thereby introducing a vulnerability analysis approach from a large-scale region segmentation perspective. This approach significantly advances the assessment of planar network vulnerability. Our findings offer practical implications for the planning and emergency management of planar networks, such as transportation systems, and provide a foundational basis for improving network security and efficiency.