Robustness of higher-low order networks with adjustable coupling strength

Abstract

Robustness is one of the most critical characteristics of complex networks, determining their stability and resilience in the face of various disturbances. With the research on complex networks, people have observed that higher-order networks can also affect the structure and function of the network. Therefore, when studying network robustness, we also need to consider the interaction between higher-order networks and low-order networks. To delve deeper into the investigation and comprehension of robustness in complex networks, this paper introduces a model of higher-low order networks with adjustable coupling strength. In this model, network nodes are categorized into autonomous and nonautonomous nodes, with coupling strength adjusted using three methods: random coupling, degree-related coupling, and local coupling. Validation is performed on ER networks, BA networks, SW networks, as well as several real-world networks. The results indicate that as coupling strength increases, network robustness correspondingly diminishes, and the network exhibits intricate percolation behavior.