## 4 Results
### Scenario Evaluation Outcomes
The fact that the vulnerability scenario ranks between the degree and the betweenness scenarios in terms of connectivity suggests that prioritizing vertiport placement based on vulnerability may lead to higher network connectivity than scenarios that allocate vertiports based solely on centrality measures. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ratio** & \begin{tabular}{c} **Betweenness UAM** \\ **Network** \\ \end{tabular} & \
\begin{tabular}{c} **Degree UAM** \\ **Network** \\ \end{tabular} &
\begin{tabular}{c} **Vulnerable UAM** \\ **Network** \\ \end{tabular} \\ \hline
5\% & 17.3005 & 16.0882 & 15.8778 \\
10\% & 12.2384 & 11.9723 & 10.6847 \\
15\% & 9.7350 & 9.8296 & 8.2023 \\
20\% & 8.7287 & 7.3651 & 7.0458 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average shortest path length results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ratio** & \begin{tabular}{c} **Betweenness UAM** \\ **Network** \\ \end{tabular} & \
\begin{tabular}{c} **Degree UAM** \\ **Network** \\ \end{tabular} &
\begin{tabular}{c} **Vulnerable UAM** \\ **Network** \\ \end{tabular} \\ \hline
5\% & 0.08706 & 0.08948 & 0.09556 \\
10\% & 0.12753 & 0.12932 & 0.14703 \\
15\% & 0.16842 & 0.16566 & 0.19674 \\
20\% & 0.19971 & 0.21665 & 0.23825 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Network global efficiency results. The baseline network has a low local clustering coefficient, making it closer to a tree-structured random network. When vertiports are installed, the clustering coefficient increases across all scenarios compared to the baseline network, indicating a significant impact of intentional vertiport placement. Among the scenarios, the betweenness scenario exhibits the highest clustering coefficient, though the difference compared to the other scenarios is not substantial. Table 6 illustrates these changes in the clustering coefficient. Table 7 presents the transitivity index, which reflects the overall clustering of the network, in contrast to the clustering coefficient. In the scenario where 5% of all stations are equipped with vertiports, the betweenness scenario records the highest transitivity value at 0.91335, followed by the degree scenario (0.89679) and the vulnerability scenario (0.87188). Notably, these values represent a 380% increase from the baseline network's transitivity index of 0.18, indicating that vertiport installation enhances clustering across the entire network. This suggests that the network structure may transition into a small-world network, which aligns with the expectation that vertiport implementation leads to shorter average path lengths. In the 20% vertiport installation scenario, transitivity approaches 1, further reinforcing the small-world network characteristics, suggesting a stronger clustering effect as vertiport density increases. The modularity index, which evaluates the community structure of the network, is 0.879 in the baseline network. When vertiports are installed at 5% of all stations, the modularity decreases to a range of 0.657-0.688, and as the installation rate increases to 20%, it further declines to 0.609-0.771 (Table 8). This indicates a sharp decrease in modularity as vertiport placement increases. This trend suggests that while urban rail networks traditionally maintain strong community structures along individual lines, the installation of vertiports accelerates inter-community connections, diminishing the network's tendency to form small, isolated \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ratio** & \begin{tabular}{c} **Betweenness UAM** \\ **Network** \\ \end{tabular} & \
\begin{tabular}{c} **Degree UAM** \\ **Network** \\ \end{tabular} &
\begin{tabular}{c} **Vulnerable UAM** \\ **Network** \\ \end{tabular} \\ \hline
5\% & 0.91335 & 0.89679 & 0.87188 \\
10\% & 0.97169 & 0.96848 & 0.95549 \\
15\% & 0.98427 & 0.98409 & 0.97476 \\
20\% & 0.98920 & 0.98782 & 0.98188 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Network transitivity results.