Fig. 1. Dependencies among power infrastructures^[9].

Fig. 2. Modeling of cascading failure iterative processes^[10]: (a) The network is attacked in the initial state; (b), (c), and (d) are the cascading failure processes of the network due to the dependencies between dependent networks after the attack, respectively. Eventually reached a steady state.

Fig. 3. Nodes protection model based on interdependent networks^[17].

Fig. 4. Illustration of failure recovery strategy^[14]. The giant components of network A and network B are shown in the figure. Case 1: Two failed nodes (nodes 1 and 2) connected by dependent edges are respectively at a distance of l= 1 from their maximal cluster, and then repaired with recovery probability γ. Case 2: If at least one of the two interdependentdent failed nodes (nodes 3 and 5) is more than 1 away from its maximal cluster, the recovery condition is not met, so the pair of nodes is abandoned to be restored.

Fig. 5. Schematic diagram of the implementation of recovery strategy in network B^[67]: (a) GC represents the giant component of the network, the dashed lines indicate idle connected edges, clusters with free connected edges repre-sent repairable clusters, and clusters without free connected edges represent clusters that cannot be recovered; (b) the giant component of network B after reconnection.

Fig. 6. Schematic diagram of recovery model.