The Target Recovery Strategy for Preventing Avalanche Breakdown on Interdependent Community Networks

Figure 3

An example of the recovery strategy based on community structures. There are two pairs of mutual boundary nodes, (a₁, b₁) and (a₂, b₂), in subnetwork A and subnetwork B. The purple circles belong to the community m₁, the green circles belong to m₂, the orange circles belong to m₃, and the black circles mean failed nodes that have no direct connection to the GC. In this example, the parameter β is assigned to 0.3. The value of R(a₁, b₁) = 3.1 is computed by k_intra, the number of inactive intracommunity links that are connected to the GC (black-dotted lines), and k_inter, the number of inactive intercommunity links that are connected to the GC (yellow dotted lines) for the nodes a₁ and b₁. The example assigns k_intra(a₁) = 2, k_inter(a₁) = 1, k_intra(b₁) = 2, and k_inter(b₁) = 0. The value of R(a₂, b₂) = 1.7 is computed in the same way. The results of R(a₁, b₁) and R(a₂, b₂) show that the pair of nodes a₁ and b₁ needs to be recovered. Furthermore, the links (black- and yellow-dotted lines) of a₁ and b₁ within their GC are restored.