## 4 Case Study
### Simulation Analysis of Restorative Measures  
In this section, based on the previously described simulation algorithm, network efficiency is adopted as the evaluation metric, while the number of recovered nodes is used in place of the time variable to assess the progress and effectiveness of network recovery. Simulations are conducted on China's railway service network under four major types of disturbance events: external attacks, natural disasters, technical malfunctions, and fluctuations in passenger and freight traffic. After the disturbance, failed nodes are removed from the network for restoration. The betweenness recovery strategy, degree recovery strategy, and random recovery strategy are employed to explore which performs optimally under different disturbance states. Firstly, the external attack is simulated to remove the failed nodes in the network, with the number of failed nodes removed set at 100. The results are shown in Figure 12.  
Figure 11: Network resilience invulnerability trend graph. Figure 12: Network efficiency recovery diagram under external attack simulation. The network efficiency of the service network when it is not disturbed is 0.68524, and it drops to 0.4447 after being perturbed by external attacks. During the recovery process, the network efficiency demonstrates an overall upward trend. Among the three strategies, the betweenness centrality-based recovery strategy (green line) demonstrates the most stable and substantial improvement. This indicates that restoring critical \"bridging\" nodes--those with high betweenness--has the most significant impact on enhancing network efficiency, as it quickly reestablishes overall connectivity. The degree recovery strategy (blue line) comes next, showing a certain degree of efficiency fluctuation but presenting an overall stable upward trend. Although the node degree is an important structural indicator, it is less effective than betweenness in restoring network performance. Nodes with high degree values may have numerous connections but may not be located on the critical paths of the network. The random recovery strategy (red line) has the largest fluctuations, indicating that randomly selecting nodes for network recovery is the least efficient approach. This strategy neglects the characteristics of the network structure and is thus insufficiently effective in improving the network efficiency. Secondly, the failure nodes in the network were removed to simulate the fluctuations of passenger and cargo traffic. The number of removed failure nodes was set at 100, and the results are presented in Figure 13.  
The network efficiency of the railway service network was 0.68524 under undisturbed conditions, which dropped to 0.35204 following disturbances caused by fluctuations in passenger and cargo traffic. On the whole, the recovery efficiencies of the three strategies all gradually rose, but the recovery efficiency of the betweenness centrality recovery strategy (the green line) was significantly higher than the speed and level of efficiency improvement of the other two strategies. This finding further reinforces the critical role of nodes with high betweenness centrality in restoring overall network functionality. Such nodes are typically located at structurally important positions and serve as key connectors between different regions of the network. Although the efficiency improvement of the degree value recovery strategy (the blue line) was stable, its growth rate and peak were lower than those of the betweenness centrality recovery. This is likely because nodes with high degree values, though possessing numerous connections, may not occupy strategically central positions within the network. The efficiency growth of the random recovery strategy (the red line) was the slowest, indicating that randomly selecting nodes to restore the network is the least efficient approach. This strategy fails to consider the significance of the network topology and the strategic positions of nodes, leading to suboptimal recovery effects.