## 5 Conclusions and Discussion  
Complex network and temporal network theories were employed to explore the temporal and topological characteristics of the CATN. The network was defined as a dynamic temporal network and was mapped into a static network using time windows. The results indicated that the aviation network primarily operated from 6:00 to 24:00, with peak hours at 7:00 and 10:00. During these hours, the network exhibited an obvious scale-free characteristic and a small-world phenomenon, with the degree distribution rising rapidly in the initial stages before gradually stabilizing and finally rapidly dropping after the peak hours. Before final stabilization, the distribution of clustering coefficients initially increased and then decreased. The average shortest path showed that 80% of paths passed through  
Figure 14: Temporal changes in the size of the maximum connected component and network efficiency of four specific time intervals: (**a**) attacking 5 nodes at once at 6:00, 12:00, 18:00, and 24:00; (**b**) attacking 10 nodes at once at 6:00, 12:00, 18:00, and 24:00.  
hub airports, with an obvious central radiation structure. Furthermore, the robustness of the CATN at different times against random and deliberate attacks was explored using the proportion of maximum connected sub-graph nodes and network efficiency as robustness measures. The network was weak under deliberate attacks, particularly when using betweenness centrality and closeness centrality strategies. Further, it was observed that the CATN exhibited temporal unevenness in centrality, often leading to changes in the shortest path.  
As a preliminary study, the feasibility of temporal network theory in CATN research was verified, and the law of robustness variation in the CATN was discussed. In our future research, an in-depth exploration will be conducted from two perspectives. First, the theory of temporal networks will be employed to investigate the intricate dynamics of networks in the CATN, aiming to provide practical solutions for optimizing flight schedules. This involves addressing cascading failures triggered by nodes or links within the network, as well as the dispersion and propagation of delays. Second, an exploration of more advanced techniques for temporal network modeling will be undertaken, aiming to accurately capture the dynamic structure of the CATN. Event-based temporal networks or dynamic graph neural networks can be utilized for this purpose.  
Conceptualization, R.Y. and W.S.; data curation, W.S.; formal analysis, R.Y.; funding acquisition, H.Z.; methodology, R.Y. and W.S.; resources, R.Y.; supervision, H.Z.; validation, R.Y., M.L. and H.Z.; visualization, W.S.; writing--original draft, R.Y. and W.S.; writing--review & editing, M.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Hainan Provincial Natural Science Foundation of China (grant number 2019 RC199) and the National Natural Science Foundation of China (grant number 62167003).  
Not applicable.  
The data and material used in this study were obtained from VariFlight. Due to the commercial nature of the data, access to the data is restricted by the provider. However, we have obtained the necessary permissions and licenses to use the data for our research study.  
We gratefully acknowledge the financial support provided by the Hainan Provincial Natural Science Foundation of China (grant number 720 RC616) and the National Natural Science Foundation of China (grant number 62167003).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CATN & Chinese aviation temporal network \\ CAN & Chinese temporal network \\ \end{tabular}