## 3 Case Study
### Result Analysis
#### 3.3.2 Comprehensive Evaluation of Node Importance  
The comprehensive node ranking results of each node, calculated using Equation (17) and Equation (18), are shown in Figure 7. \begin{table}
\begin{tabular}{c c c c} \hline
**Network** & **Indicator** & **Most Important Node(s)** & **Observations** \\ \hline \multirow{4}{*}{LC} & CS & 6–18 DG & \multirow{4}{*}{Different indicators result in varying node rankings. Nodes like 13 DG, 19/53 WG, D7G, \\  & DNC & B1G & \\  & SNC & TF3G, TF4G & \\  & NE & 37–47 DG & D9G rank consistently low. \\  & EPR & 3–5 DG & \\ \hline \multirow{4}{*}{YX} & CS & 27–33 DG, 29–31 DG & \multirow{4}{*}{Rankings vary by indicator but show bimodal distribution. Left-side nodes are more important due to down-throat routes.} \\  & DNC & 55–61 DG & \\  & SNC & IIIAG & \\  & NE & 27–33 DG & \\  & EPR & 29–31 DG & \\ \hline \multirow{4}{*}{DC} & CS & 6–18 DG & \multirow{4}{*}{Left- and right-side nodes are more important than central nodes. Rankings are relatively consistent across parameters.} \\  & DNC & 51 DG, 53–63 DG, 65 DG & \\  & SNC & 1–7 DG, 3–5 DG, 9 DG (and six others) & \\  & NE & 11–23 DG & \\  & EPR & 37–47 DG & \\ \hline \end{tabular}
\end{table} 
Table 2: The summary of the analysis results for the LC, YX, and DC networks. Figure 7 illustrates the comprehensive ranking results of each node in the network. The horizontal axis represents the node identifiers, while the vertical axis denotes the comprehensive ranking values, derived from multiple evaluation criteria. The visualization employs distinct markers and color coding to differentiate node ranking distributions across the network. * High-ranking nodes (depicted by red circles) exhibit significantly higher-ranking values, indicating their dominant influence within the network. These nodes are concentrated in specific regions, suggesting their crucial role in maintaining network connectivity and operational efficiency;
* Moderate-ranking nodes (represented by orange squares) demonstrate intermediate ranking values, implying their transitional function within the network. The variability in their rankings across different regions reflects heterogeneous connectivity patterns;
* Low-ranking nodes (shown as blue diamonds) consistently display lower-ranking values, indicating limited structural influence within the network. These nodes likely function as secondary connectors rather than primary operational hubs. The ranking distribution suggests a hierarchical network structure, where specific nodes exhibit dominant connectivity and operational significance, while others primarily serve as supporting links. The interspersed distribution of high-ranking and low-ranking nodes highlights potential structural inefficiencies or bottlenecks, necessitating further optimization to enhance overall network resilience and performance. This ranking analysis provides valuable insights into node importance, facilitating data-driven infrastructure optimization and operational planning. Future research could integrate dynamic network simulations to further validate these rankings under varying operational scenarios. Figure 8 presents the spatial distribution of the comprehensive ranking results of each node within the railway station network. This visualization integrates the ranking outcomes obtained in the previous analysis (Figure 7) and maps them onto their respective physical locations within the railway yard. The diagram highlights the relative importance of different nodes in terms of connectivity, operational efficiency, and structural significance. Figure 7: Comprehensive ranking distribution of network nodes. The ranking results are categorized into three levels and are visually distinguished using different symbols and colors:  
* Level 1 (high-ranking nodes, red circles): These nodes exhibit the highest ranking values, indicating their crucial role in network connectivity and train operations. They are predominantly located in station throat areas, where train routing decisions and operational flexibility are most critical.