## 2 Related Work
### The Construction of Railway Complex Network Model and the Fundamental Theory of Resilience
Restorability, on the contrary, focuses on the ability to repair the damaged infrastructure and restore it to its original service level after the fault is resolved or the disturbance event concludes. The higher the resilience of the system, the shorter the time required for both adaptation and recovery; conversely, prolonged response and restoration times indicate lower resilience. To provide a theoretical foundation for our resilience measurement system, we integrate insights from established transportation resilience research. Our three-dimensional framework (accessibility, invulnerability, and restorability) is grounded in complementary theoretical perspectives from the literature. The accessibility dimension builds upon [PERSON] et al. 's identification of accessibility as a fundamental component of transportation resilience, while [PERSON] [21] emphasized the critical role of topological connectivity in network resilience analysis. The invulnerability dimension draws from [PERSON]'s [4] conceptualization conceptualization of vulnerability as a network's sensitivity to disruptions that significantly reduce service capacity, with [PERSON] et al. [22] providing the theoretical basis for our cascade failure model by defining vulnerability as the performance level maintained during disturbances. The restorability dimension incorporates [PERSON] et al. 's [23] distinction between static and dynamic resilience, with the latter focusing on a system's ability to efficiently return to normal operations after major disturbances. [PERSON] et al. 's resilience metrics, which simultaneously measure recovery speed and cumulative network performance loss, align with our methodological approach. Together, these three dimensions provide a comprehensive assessment of railway network resilience throughout the entire disruption-to-recovery cycle, consistent with [PERSON] et al. 's definition of urban transportation resilience as both a system's ability to resist, mitigate, and absorb various disturbances and its capacity to restore normal operations within reasonable time and cost constraints. As illustrated in Figure 2, a resilience measurement system covering the various stages of operation, defense, buffering, damage, and recovery is constructed by taking the three evaluation dimensions as the vertices:  
Next, detailed explanations will be provided for the definitions of these three measurement indices and the network performance they describe:  
1. The accessibility measure of railway network resilience reflects the capacity of the railway network to maintain the interconnection among all parts of the network and ensure the normal operation of transportation functions when confronted with various disturbances. It primarily concerns the extent to which effective connections between stations can still be established through available paths when the network is subjected to specific disruptions. The accessibility measure is directly related to the ability of the railway network to continuously provide basic transportation services when encountering disturbances and is a crucial indicator for assessing the resilience of the railway physical network. 2. The invulnerability measure of railway network resilience gauges the extent to which the network structure of the railway network can be sustained and the degree of impairment of network functions after withstanding disturbances of a specific intensity. It reflects the network's capacity to sustain connectivity under external shocks, as well as its ability to redistribute and reconfigure traffic flows. The invulnerability measure embodies the stability of the railway physical network when confronted with severe disturbances and is a crucial parameter for determining the network's capacity to resist external attacks. 3. The restorability measure of railway network resilience focuses on the speed and efficiency with which a railway network resumes its normal operational status after encountering a disturbance.