Robustness of higher-order network pertinent to first- and higher-order dependency

Robustness of higher-order network (HON) with dependency is different from first-order network (FON), as the attack orders and the number of iterations are totally different. To measure the robustness of HON with dependency, this study proposed new attack strategies on node and edge failure through measuring the size of the giant component and global efficiency. And two real-world systems of hazardous materials transportation accident causation system and Chinese high-speed railway system with different network size were empirically studied. Results show that HON is more fragile to robustness attacks than FON. The number of attack iterations is uncertain in HON, which depends on the attack strategies and the network structure. Meanwhile, nodes and edges with high dependency have greater impacts on network robustness, providing valuable insights into capturing critical information. This study may be helpful to design the robust system, improve the system's reliability and serve as a valuable reference for future exploration of HONs robustness.