The effect of interdependence on the percolation of interdependent networks

Two stochastic models are proposed to generate a system composed of two interdependent scale-free (SF) or Erdős–Rényi (ER) networks where interdependent nodes are connected with an exponential or power-law relation, as well as different dependence strength, respectively. Each subnetwork grows through the addition of new nodes with constant accelerating random attachment in the first model but with preferential attachment in the second model. The two subnetworks interact with multi-support and undirectional dependence links. The effects of dependence relations and strength between subnetworks are analyzed in the percolation behavior of fully interdependent networks against random failure, both theoretically and numerically, and as a result, for both relations: interdependent SF networks show a second-order percolation phase transition and the increased dependence strength decreases the robustness of the system, whereas, interdependent ER networks show the opposite results. In addition, the power-law relation between networks yields greater robustness than the exponential one at the given dependence strength.