## 4 Discussion
### Analysis of Indicators for Evaluating Key Nodes
From Figure 11, the following conclusions can be drawn:  
* LC network exhibits consistently low NE values, indicating high structural redundancy, where no single node is critical;  
Figure 11: Comparative analysis of NE across LC, YX, and DC networks. * YX and DC networks have higher NE peaks, suggesting greater dependency on specific nodes;
* High-impact nodes include 27-33 DG (YX, NE = 0.30) and 11-23 DG (DC, NE = 0.23), whose removal substantially reduces network efficiency. Analyzing from the perspective of structural influence, YX and DC networks are more vulnerable to node failures due to their reliance on key hubs. LC network maintains stability, suggesting a decentralized structure with fewer critical nodes. Targeted reinforcement of high-NE nodes could enhance railway network robustness and operational resilience. This analysis highlights structural differences in network resilience, where YX and DC networks rely on key nodes, while LC remains more fault-tolerant. Future work should prioritize protecting high-NE nodes and explore dynamic failure simulations for enhanced railway infrastructure planning. (4) Extended PageRank Algorithm Based on Edge Weights (EPR)  
Using Equation (15), the extended PageRank (EPR) values for each node in the various network layers were calculated, as shown in Figure 12. It presents the EPR values for each node in the LC, YX, and DC networks, where EPR is computed based on edge weights to quantify node importance in the network. The horizontal axis represents network nodes, while the vertical axis denotes the EPR values. Each network layer is represented by a distinct color:  
* LC network (red circles, top panel);
* YX network (orange squares, middle panel);
* DC network (blue diamonds, bottom panel). The pink-shaded regions represent nodes whose EPR values fall within one standard deviation above or below the mean, providing a reference for identifying statistical outliers. Analyzing from the perspective of structural influence, the LC network shows a more balanced node influence distribution, with fewer extreme variations, indicating a robust structure with less reliance on individual nodes. The YX network has the most concentrated EPR distribution, meaning most nodes contribute similarly to overall connectivity, except for the high-impact outlier (29-31 DG). The DC network exhibits moderate fluctuations, with a few nodes deviating significantly from the mean, highlighting localized structural importance. Nodes with high EPR values in each network act as key hubs, playing a crucial role in maintaining network stability and connectivity. Figure 12: Comparative analysis of EPR across LC, YX, and DC networks. This comparative analysis highlights differences in node importance across the three network layers:  
* LC has a more evenly distributed node influence, ensuring greater resilience;
* YX has a dominant high-EPR node, indicating centralized connectivity;
* DC exhibits moderate variability, with a few critical nodes driving network stability. Future research could integrate real-world train movement data to assess the practical implications of high-EPR nodes on railway operations.