Research on the connection radius of dependency links in interdependent spatial networks against cascading failures

Most of previous research on complex networks always concentrates on topology, ignoring the coordinates of components. However, the spatial information of components may be a key factor influencing the invulnerability of actual networks. For interdependent infrastructures, considering space constraints, dependency links may be established locally, where only nodes within certain connection radius rconnect can be connected as dependent node pairs. Therefore, based on the topology-based cascading failure model, the invulnerability of interdependent scale-free networks is studied by introducing five coupling patterns in this paper, including global and local random couplings GR and LR, global and local degree-degree inter-similarity couplings GD and LD and nearest neighbor coupling NN. Under topological attacks, the inter-similarity couplings GD and LD have better performance, and as rconnect increases, the effect of LD will gradually approach to GD. In order to ensure a good invulnerability and low construction cost, a novel hybrid coupling pattern of NN and LD is proposed. With numerical simulations, we find that selecting nodes with large degree to establish LD coupling has significant effect, and there is an optimal selection fraction. Under localized attacks, the local couplings perform better, and LD is better for small rconnect while NN is better for large rconnect. In addition, we also study a simplified localized attacking strategy analytically based on percolation theory, which is proved to be consistent with the numerical results. For LD coupling, the effect will be influenced by rconnect, and there are minimum and maximum invulnerability values for topological and localized attacks, respectively. These findings can help to understand the characteristics of spatially embedded interdependent infrastructures.