## 4 Robustness of the CATN
### Influence of Structure on CTAN Robustness  
This study performed attack experiments on four network snapshots employing centrality metrics as outlined in Section 2. In each experiment, only a single node was targeted, allowing us to investigate the alterations in the maximum connected component when employing both centrality-based and random attack strategies. As the number of deleted nodes increased, the proportion of nodes in the maximum connected component exhibited a significant downward trend (Figure 12). Random attacks were not effective in disrupting the connectivity of the aviation network in all four time intervals. On the  
Figure 11: Temporal changes in closeness centrality. The blue represent the top 15 airports with high closeness centrality, while the remaining airports are depicted in black. Figure 10: Temporal changes in betweenness centrality. The blue represent the top 15 airports with high nearest neighbor degree centrality, while the remaining airports are depicted in black. containtainly, the ability of the nearest neighbor degree attacks to rapidly identify crucial nodes in the aviation network, specifically hub airports. However, the subsequent attack effects were not significant and were comparable to random attacks. Referring to the findings in Figure 9, it can be inferred that the nearest neighbor degree attack primarily targets regional hub airports. Although these attacks do not result in a widespread paralysis of the aviation network, the transportation capacity of the network will diminish rapidly. Betweenness and closeness centrality-based attacks were more vulnerable. The uneven temporal distribution of the CATN led to frequent changes in the shortest paths. As both betweenness and closeness centrality indicators were related to the shortest path, safeguarding the hub airports located on the shortest path was necessary to ensure the connectivity of the aviation network. Network efficiency, represented by \(E\), was another indicator for evaluating the robustness of the network under attack. Similar to the analysis conducted on giant components, attacks were carried out by targeting only one node at a time. Specifically, centrality and random attacks were performed on the CATN, and the alterations in CATN efficiency were observed across four time intervals. The attack results are exhibited in Figure 13. Random  
Figure 12: Temporal changes in the size of the maximum connected component in four specific time intervals: (**a**) the relationship between the relative size of the maximum connected component and the proportion of deleted nodes at 600, (**b**) the relationship between the relative size of the maximum connected component and the proportion of deleted nodes at 12:00, (**c**) the relationship between the relative size of the maximum connected component and the proportion of deleted nodes at 18:00, and (**d**) the relationship between the relative size of the maximum connected component and the proportion of deleted nodes at 24:00.  
attacks were ineffective, so the efficiency did not decrease. Degree-based attacks and nearest neighbor degree attacks produced similar results with the size of the maximum connected component. Betweenness and closeness attacks, however, caused considerable damage to the aviation network. After removing 10% of the airports, the efficiency decreases by nearly 20% of the initial value, and the network gradually collapsed. By using the same attack strategy, it was observed that network efficiency was more substantially affected than the maximum connected component. This suggested that, although the aviation network could remain connected with a good network topology after an attack, its efficiency was greatly reduced. As a result, while the aviation network was possibly accessible topologically, it remained disconnected in a temporal sense. In the aforementioned experiment, the authors employed a single-node attack approach.