## 4 Case Study  
### Experimental Design and Parameter Setting  
(1) Experimental Design  
Through the collection and screening of relevant materials, this study conducted a comprehensive assessment of China's railway transportation network operation routes, network structure, and overall characteristics. Based on the model assumptions established in previous sections, we constructed a physical network model of China's railway transportation system.  
The physical network model includes 978 node cities and 1434 connecting routes. These nodes represent major railway stations across the country, while the edges represent the physical rail connections between these stations. This model captures the geographical topology and physical infrastructure of China's railway network.  
When constructing the railway service network model, obtaining station information and train service data between stations became a critical step. We employed web crawling technology to effectively collect these essential data, thereby constructing a topological model of the railway passenger transportation network. This method not only ensures the timeliness and accuracy of the data but also comprehensively reflects the actual operational conditions of the railway service network.  
Using the railway timetable of September 2023 as a benchmark, we developed a web crawler program in Python (v3.10.4) to acquire relevant data of China's railway passenger transportation network from the 12306 website (China's official railway ticketing platform) and Ctrip. Based on the model assumptions described in previous sections, these data were used to construct China's railway service network model. The final model encompasses 3144 station nodes, information on 11,179 train services, and 91,678 pairs of inter-station connections.  
The subsequent simulation analysis was conducted on these two network models. The physical network model serves as the foundation for evaluating the structural resilience of the railway infrastructure, while the service network model provides insights into the operational resilience of the railway system in response to various disturbance events.  
(2) Parameter Setting  
Before proceeding with the case study, it is essential to clarify the parameter settings and weight allocation methods employed in our railway network resilience analysis. These configurations directly influence the simulation outcomes and interpretation of results.  
For the accessibility measure, we set equal weights (a = b = c = 1/3) for the three components--reachable node pairs, clustering coefficient, and network efficiency--to ensure a balanced consideration of each aspect in the overall accessibility assessment. This equal weighting approach was selected after sensitivity testing revealed that differential weighting did not significantly alter the relative performance patterns across disturbance types.  
In the cascade failure model used for invulnerability assessment, the capacity enhancement coefficient (\(\sigma\)) was set at 0.1 after calibration with historical railway disruption data. This value represents a realistic capacity buffer maintained in China's railway system based on operational practices. Sensitivity analysis confirmed that while absolute resilience values vary with different \(\sigma\) values (0.05-0.20), the relative resilience patterns across disturbance types remain consistent ([PERSON]'s W = 0.89, \(p\) < 0.001).  
For the recovery simulation, we standardized the number of failed nodes at 100 (approximately 10% of the network nodes) across all disturbance scenarios to facilitate meaningful comparisons between different recovery strategies. This threshold was determined through preliminary testing to represent a significant but manageable disruption level, allowing for observable differences in recovery performance without complete network collapse.