## 3 Case Study
### Result Analysis  
#### 3.3.1 Hierarchical Evaluation of Node Importance Based on Single Indicators  
Figures 4-6 present the computational analysis results for the LC, YX, and DC networks, respectively. The horizontal axis represents all track sections within the RSCN. Notably, the left and right ends of the axis correspond to the upward and downward throats of the station, which serve as critical hubs for train operations. The results are visualized using a color gradient ranging from red (top-level indicators) to blue (bottom-level indicators), highlighting different analytical perspectives. Figure 4: The computational results for the LC network, listed from top to bottom, are as follows: CS, DNC, SNC, NE, and EPR. Figure 3: The RSCN is structured from top to bottom as follows: the LC, YX, and DC networks. In Figure 4, a detailed computational analysis of the LC network is presented, highlighting variations in key indicators across different nodes:  
* The CS curve exhibits significant fluctuations, indicating pronounced heterogeneity in connection strength across different nodes. Notably, the values peak in the upward and downward throat areas, suggesting that these critical regions exhibit markedly enhanced connectivity strength, likely due to their pivotal role in railway yard operations;
* Both DNC and SNC curves show localized peaks at specific nodes, highlighting their central role in network connectivity. These high-value nodes are likely associated with key functional areas, such as entry and exit points of arrival/departure tracks, where train flow is concentrated;
* NE remains relatively stable throughout the network but experiences minor declines at certain nodes. These localized reductions suggest the presence of structural inefficiencies, which may hinder overall operational performance by limiting network throughput or increasing transit delays;
* The EPR distribution exhibits distinct local extrema, indicating substantial variations in node rankings based on edge weights. These fluctuations underscore the presence of structurally dominant nodes that disproportionately influence network dynamics, reflecting their critical importance in real-world railway operations. Figure 5: The computational results for the YX network, listed from top to bottom, are as follows: CS, DNC, SNC, NE, and EPR. Figure 6: The computational results for the DC network, listed from top to bottom, are as follows: CS, DNC, SNC, NE, and EPR. Figure 5 illustrates the computational analysis of the YX network, revealing distinct structural and functional characteristics across different metrics:  
* The CS distribution closely aligns with the trend of the DNC. Notably, in the left-side downward throat area, both CS and DNC values are significantly higher than in other regions, indicating intensified interactions and an increased network load in these critical zones;
* Similarly, the SNC and NE curves exhibit a high degree of consistency. In particular, the left-side downward throat area and the central arrival-departure yard show higher SNC and NE values compared to the downward throat region. This pattern may reflect a well-defined functional zoning within the yard. Such systematic organization of node interactions could have a significant impact on train dispatching and operational efficiency;
* The EPR curve displays distinct peaks, suggesting that local variations in node connectivity strongly influence the edge-weighted ranking. Additionally, nodes on the left side are generally more influential than those on the right. This dominance is primarily due to the YX routing structure, which includes only the downward throat area and certain track sections in the arrival-departure yard. As a result, nodes in this region hold greater structural weight within the network.