Percolation behaviors of partially edge-coupled interdependent networks

Most previous researches on interdependent networks are based on node-coupled interdependency. Considering the mutual interaction between some edges among multi-layer networks in the real world, a model of partially edge-coupled interdependent networks is established and the corresponding theoretical analysis framework is developed based on the self-consistent probability theory. The percolation behaviors and the percolation thresholds of the partially edge-coupled interdependent networks composed of Random Regular networks and the Erdös–Rényi networks are analyzed and verified by simulations. We find that the edge-coupled interdependent networks become stronger as the decreases of coupling strength, and the phase transition process also shows a transition from a first-order to a second-order, which is the same as the corresponding partially node-coupled interdependent networks. Other than that the critical value of coupling strength qc that distinguishes the first-order and second-order is also the same as the node-coupled one. However, the phase transition threshold of the edge-coupled model is smaller than that of the corresponding node-coupled which means a more robust system. Our findings are of great significance for understanding the robustness of partially edge-coupled networks in the real world.