## 3 Empirical Analysis
### Topological Properties of the CATN
#### 3.2.4 Temporal Property of Clustering Coefficient  
The clustering coefficient is a feature that can be applied to connected graphs. However, when time slicing was applied to the CATN, some graphs in certain time periods became disconnected, which largely consisted of a connected sub-graph and one to three small connected sub-graphs with no more than three airports, which were all branch airports. Hence, the small connected sub-graphs were ignored when calculating the clustering coefficient, and only the maximum connected sub-graph was taken into consideration.  
The average clustering coefficient (C) of the network can reflect the overall network characteristics. Figure 7 exhibits that this topological feature demonstrates substantial fluctuations from 6:00 to 9:00 and after 22:00, signifying considerable alterations in the network structure during these periods. The clustering coefficient remained at a high and stable value from 9:00 to 21:00. When combined with the average shortest path, the CATN demonstrated significant small-world characteristics with high clustering and short distances. The network structure in the early morning consisted of scattered flight routes that did not create a significantly connected sub-graph. As additional airport nodes and flight routes joined the network over time, its structure became increasingly complicated, which resulted in a rapid rise in the clustering coefficient between 5:00 and 7:00, and a subsequent sharp decrease from 7:00 to 9:00. This phenomenon can be attributed to a temporal asymmetry in the rate of growth between routes and airports within the network during distinct time intervals. Specifically, during the period from 5:00 to 7:00, the rate at which routes become part of the network surpasses the rate at which airports are incorporated. In contrast, between 7:00 and 9:00, the rate at which routes integrate into the network lags behind the rate at which airports join.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Shortest Path** & \begin{tabular}{c} **Number of Flights** \\ **Needed to Change** \\ \end{tabular} & \
\begin{tabular}{c} **Number** \\ **of Paths** \\ \end{tabular} &
\begin{tabular}{c} **Percentage of** \\ **Air Routes** \\ \end{tabular} \\ \hline
1 & 0 & 7156 & 13.59\% \\
2 & 1 & 40,118 & 76.17\% \\
3 & 2 & 5396 & 10.24\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Distribution of air routes based on the number of flights.  
Figure 6: Spatiotemporal features of the aviation network at four specific time intervals. In the provided graph, the size of the nodes corresponds to the degree of those nodes. The color bar in the legend represents different value of normorlized degree. Each color corresponds to a specific range of values.  
The findings of this study revealed the dynamic nature of the network through the examination of the degree and clustering coefficient. The analysis of the temporal and spatial variations in node degree illustrates the dynamic nature of airport operations and the fluctuating distribution of air traffic throughout the day. The fluctuation of the clustering coefficient reflects the changing patterns of connectivity and the growth of the network scale. This provides important data support for airport management and operational optimization, as well as information for the decision-making process of expanding routes and allocating airport resources to ensure effective connectivity and overall transportation performance.