Percolation of edge-coupled interdependent networks

The study of the robustness of interdependent networks has attracted enormous attention from researchers of diverse fields. For this topic, the node-dependent scheme is most widely adopted to describe the interdependency between different network layers, where nodes in one layer are interdependent with nodes in other layers. However, this scheme may not well reflect many realistic scenarios, since many real systems are actually based on a edge-coupled interdependency, that is edges in one layer are interdependent with edges in other layer. In this paper, we propose an edge-coupled interdependent networks (EIN) model to address this kind of interdependency. A mathematic framework based on a set of self-consistent equations is developed to characterize the robustness of EIN, which is further verified by extensive simulations over different kinds of network structures. It is shown that the EIN also possesses the discontinuous phase transition behavior and the threshold of the phase transition is smaller than that of node-coupled interdependent networks (NIN), which suggests a stronger robustness of EIN. Moreover, as contrast to NIN, for EIN a broader degree distribution could enhance the robustness of EIN reflected by the reducing of the threshold of transition. Our findings could help deepening the understanding of interdependent networks that are coupled with the edge perspective and pertinent real world systems.