关键词: complex networks, high-order structure, edge importance, connectivity, propagation dynamics

Abstract: Identifying important nodes and edges in complex networks has always been a popular research topic in network science and also has important implications for the protection of real-world complex systems. Finding the critical structures in a system allows us to protect the system from attacks or failures with minimal cost. To date, the problem of identifying critical nodes in networks has been widely studied by many scholars, and the theory is becoming increasingly mature. However, there is relatively little research related to edges. In fact, critical edges play an important role in maintaining the basic functions of the network and keeping the integrity of the structure. Sometimes protecting critical edges is less costly and more flexible in operation than just focusing on nodes. Considering the integrity of the network topology and the propagation dynamics on it, this paper proposes a centrality measure based on the number of high-order structural overlaps in the first and second-order neighborhoods of edges. The effectiveness of the metric is verified by the infection-susceptibility (SI) model, the robustness index R, and the number of connected branches θ. A comparison is made with three currently popular edge importance metrics from two synthetic and four real networks. The simulation results show that the method outperforms existing methods in identifying critical edges that have a significant impact on both network connectivity and propagation dynamics. At the same time, the near-linear time complexity can be applied to large-scale networks.

Key words: complex networks, high-order structure, edge importance, connectivity, propagation dynamics