## 4 Results
### Scenario Evaluation Outcomes  
The global efficiency increased in all three strategies--betweenness, degree centrality, and vulnerability--compared to the baseline network. Specifically, under the betweenness-based strategy (hereafter referred to as the betweenness scenario), global efficiency increased from approximately 0.087 to 0.200; under the degree centrality-based strategy \begin{table}
\begin{tabular}{c c c} \hline
**Category** & **Node** & **Link** \\ \hline Road Network & 153,120 & 196,850 \\ \hline Road and Railway Network & 156,354 & 338,289 \\ \hline Railway Network & 1924 & 2058 \\ \hline Urban Railway Network & 834 & 1018 \\ \hline \end{tabular}
\end{table} 
Table 1: Number of nodes and links in network data sourced from KTDB. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Group** & **Global Efficiency** & **Average Shortest Path Length** & **Algebraic Connectivity** & **Clustering Coefficient** & **Degree Assortativity** & **Transitivity** & **Modularity** \\ \hline Urban Railway Network & 0.06080 & 24.20161 & 0.00212 & 0.05422 & 0.52806 & 0.18000 & 0.87862 \\ \hline \end{tabular}
\end{table} 
Table 2: Network topology analysis result for the Seoul Metropolitan railway network. Figure 2: The urban railway network for the Seoul Metropolitan Area. (hereafter referred to as the degree scenario), it increased from 0.089 to 0.217; while under the vulnerability-based strategy (hereafter referred to as the vulnerability scenario), it increased from 0.096 to 0.238 (Table 3). The placement of vertiports based on the vulnerability scenario reduces path lengths and mitigates network fragmentation more effectively than the betweenness and degree scenarios, leading to a maximum 19% higher global efficiency. When vertiports are installed at 20% of urban railway stations, global efficiency improves by 292% compared to the baseline network, resulting in a fundamentally different network in terms of efficiency. Thus, the network under the vulnerability scenario exhibits relatively higher efficiency than those under the betweenness and degree scenarios. This suggests that prioritizing vertiport allocation at vulnerable nodes can shorten travel distances and address network fragmentation. In contrast, the betweenness scenario results in a network structure where central nodes are well-connected but with relatively lower efficiency. The degree scenario positions global efficiency between the other two strategies. An analysis of the average shortest path length without assigning weights such as link distance revealed that in the scenario where vertiports are installed at 5% of urban railway stations, the average shortest path length was 17.3005 for the betweenness scenario, 16.0882 for the degree scenario, and 15.8778 for the vulnerability scenario (Table 4). This ranking remained unchanged even with an increase in vertiport placement up to 20%. Additionally, even with vertiports installed at just 5% of urban railway stations, the average shortest path length decreased by 28.5%. As vertiport placement increased, the shortest path length continued to decrease, aligning with intuitive expectations. Similar to the minimum global efficiency index, the vulnerability scenario proved to be the most advantageous strategy from the perspective of average shortest path length. In the scenario where 5% of all stations are equipped with vertiports, the algebraic connectivity index is higher than that of the baseline network, with values of 0.00293 for the betweenness scenario, 0.00356 for the degree scenario, and 0.00326 for the vulnerability scenario (Table 5). Connectivity continues to increase as vertiport placement reach 20%, and the relative ranking among the scenarios remains unchanged. The degree scenario exhibits a relatively higher algebraic connectivity among the three strategies. The vulnerability scenario falls between the betweenness and the degree scenario in terms of connectivity.