Vulnerability analysis of China's air and high-speed rail composite express network under different node attack strategies

The current study centers on the vulnerability of the express network. It involves the development of a composite express network in China that integrates air and high-speed rail transportation, utilizing real-world data. The network's vulnerability is evaluated through simulation analysis. This study develops a model for calculating the value of node states that takes into account both the topological position and practical utility of said nodes. A node importance calculation model is developed by utilizing the information entropy theory and the pattern of cluster distribution. Two distinct strategies for node attacks have been developed: single-point failure and multiple-point failure. A system for assessing network vulnerabilities has been developed, which utilizes alterations in network structure and functional impairments to simulate and evaluate the vulnerability of the air and high-speed rail composite express network. The findings suggest that nodes exhibiting singular transportation modes and limited external connectivity are more vulnerable to cascading effects. Frequently, these nodal points are affiliated with provinces or self-governing territories that are situated in geographically remote areas and exhibit comparatively lower degrees of economic advancement. Improving the development of urban air and high-speed rail infrastructure, as well as augmenting the connectivity of air and high-speed rail express services, are essential measures to strengthen the self-risk resistance capacity of these hubs. Optimizing the network structure and modifying the internal topological and transportation coupling relationships can enhance the overall performance of the network, thereby bolstering the risk resilience of the air and high-speed rail composite express network holistically. The aforementioned discoveries offer novel perspectives for aviation enterprises and railway departments in their decision-making regarding air-rail intermodal strategies, as well as for the development of all-encompassing transportation network planning.