Impact of local coupling on the vulnerability of 2D spatially embedded interdependent networks

Real networks are always interdependent and spatially embedded. Considering the space constraint, dependency links between networks may be established not globally but locally. In this paper, we study how the spatial coupling will impact the robustness of interdependent scale-free networks located in a 2D square plane where dependent nodes are connected within a connecting radius rconnect. Besides the traditional assortative degree-degree coupling (GD) and random coupling (GR), some novel spatial couplings are also introduced, i.e., spatial assortative degree-degree coupling (SD), spatial random coupling (SR) and nearest neighbor coupling (NN). Simulation results indicate that assortative couplings, GD and SD, can improve the robustness under topological attacks while under localized attacks, NN coupling is the best one. In addition, for SD coupling under topological attacks, we find that the robustness for small rconnect decreases with rconnect from 0 to the critical value rc1, and for larger rconnect gradually increases with rconnect from rc1 to the maximum value (rconnect)max. However, opposite results will be obtained under localized attacks. These findings may be helpful to understand and analyze some real interdependent infrastructures.