Research on improving the robustness of spatially embedded interdependent networks by adding local additional dependency links

Abstract

Most of the existing research on interdependent networks always focuses on topology, without considering the component spatial information. However, for some real interdependent infrastructures, the dependency links are more likely established locally rather than globally. In this paper, we investigate the effects of local coupling patterns impacting on the robustness of interdependent networks considering spatial information. Firstly, the interdependent scale-free network is located in a 2-D square unit plane where dependent nodes falling into a circle $O_c$ with radius r are connected. Secondly, three novel local coupling patterns, including local low degree–degree coupling, local neighbor node coupling and local random coupling, are introduced. To verify they have better effects on improving the robustness, the traditional global low degree–degree coupling, global neighbor node coupling and global random coupling are selected as comparing patterns. Finally, the improving effect rank order of proposed local coupling patterns and the equilibrium point between r and effects are obtained. Specifically, under topological attacks, with the increase of r, the effects of LLD, LNN and LR always have better performance, and the equilibrium point is $r=0.2$, when $0.2<r\le 1.4$, the effects cannot be improved obviously. Under localized attacks, besides local coupling patterns are better than global ones, the equilibrium point is $r=0.3$, when $0.3<r\le 0.8$, the effects are improved faintly. With r from 0.8 to 1.4, the effects remain constants. These findings can be as a reference to improving some real interdependent infrastructures.