Spatial network disintegration with heterogeneous cost

The problem of spatial network disintegration, such as the suppression of epidemic spread and the destabilization of terrorist networks, has garnered increasing interest. However, current methodologies often assume uniformity in disintegration costs across diverse areas, thereby simplifying the complexities of real-world scenarios. In reality, the costs of removing areas vary significantly due to geographical, economic, and structural differences. Here we draw attention to the spatial network disintegration with heterogeneous cost, where the disintegration cost to remove each area might be non-identical. We first develop a cost-constrained model based on the geospatial characteristics and introduce four typical strategies to identify crucial areas that maximize the effectiveness of the disintegration process. Experimental results on both synthetic and real-world networks indicate that while the effectiveness of the hub strategy can deteriorate under certain conditions, the average degree and leaf strategies may exhibit enhanced disintegration effects under specific parameters. This phenomenon fundamentally alters the identification of critical areas as disintegration costs transition from homogeneity to heterogeneity. These findings substantially enhance our understanding of spatial network robustness and provide a novel viewpoint for the protection of spatial networks.