Greedy control of cascading failures in interdependent networks

Optimizing the robustness of higher-low order coupled networks

Enhancing the robustness of complex networks is of great practical significance as it ensures the stable operation of infrastructure systems. We measure its robustness by examining the size of the largest connected component of the network after initial attacks. However, traditional research on network robustness enhancement has mainly focused on low-order networks, with little attention given to higher-order networks, particularly higher-low order coupling networks(the largest connected component of the network must exist in both higher-order and low-order networks). To address this issue, this paper proposes robust optimization methods for higher-low order coupled networks based on the greedy algorithm and the simulated annealing algorithm. By comparison, we found that the simulated annealing algorithm performs better. The proposed method optimizes the topology of the low-order network and the higher-order network by randomly reconnecting the edges, thereby enhancing the robustness of the higher-order and low-order coupled network. The experiments were conducted on multiple real networks to evaluate the change in the robustness coefficient before and after network optimization. The results demonstrate that the proposed method can effectively improve the robustness of both low-order and higher-order networks, ultimately enhancing the robustness of higher-low order coupled networks.

Fragility Induced by Interdependency of Complex Networks and Their Higher-Order Networks

The higher-order structure of networks is a hot research topic in complex networks. It has received much attention because it is closely related to the functionality of networks, such as network transportation and propagation. For instance, recent studies have revealed that studying higher-order networks can explore hub structures in transportation networks and information dissemination units in neuronal networks. Therefore, the destruction of the connectivity of higher-order networks will cause significant damage to network functionalities. Meanwhile, previous works pointed out that the function of a complex network depends on the giant component of the original(low-order) network. Therefore, the network functionality will be influenced by both the low-order and its corresponding higher-order network. To study this issue, we build a network model of the interdependence of low-order and higher-order networks (we call it ILH). When some low-order network nodes fail, the low-order network's giant component shrinks, leading to changes in the structure of the higher-order network, which further affects the low-order network. This process occurs iteratively; the propagation of the failure can lead to an eventual network crash. We conducted experiments on different networks based on the percolation theory, and our network percolation results demonstrated a first-order phase transition feature. In particular, we found that an ILH is more fragile than the low-order network alone, and an ILH is more likely to be corrupted in the event of a random node failure.