A method of identifying key nodes in complex networks based on weighted cycle ratio

In the face of the surge of air transport demand and the increasing risk of flight conflicts, it is very important to effectively manage flight conflicts and accurately identify key conflict aircraft. This paper presents a novel method for identifying critical nodes in flight conflict networks by integrating complex network theory with a weighted cycle ratio (WCR). By modeling aircraft as nodes and conflict relationships as edges, we construct a flight conflict network where the urgency of conflicts is reflected in edge weights. We extend the traditional cycle ratio (CR) concept to propose the WCR, which accounts for both the topological structure of the network and the urgency of conflicts. Furthermore, we combine the WCR with node strength (NS) to form an adjustable mixed indicator (MI) that adaptively balances the importance of nodes based on their involvement in cyclic conflict structure and their individual conflict strength. Through extensive simulations, including node deletion experiments and network robustness analyses, we demonstrate that our method can precisely pinpoint critical nodes in flight conflict networks. The results indicate that regulating these critical nodes can significantly reduce network complexity and conflict risks. Importantly, the effectiveness of our method increases with the complexity of the flight conflict network, making it particularly suitable for scenarios with high aircraft density and complex conflict patterns. Overall, this study not only deepens the theoretical understanding of complex aviation network analysis but also provides a practical tool for improving air traffic control efficiency and safety, thereby contributing to achieving more environmentally friendly and sustainable air transportation.