## 3 Empirical Analysis
### Topological Properties of the CATN
#### 3.2.1 Temporal Attributes of Nodes and Edges  
The temporal variation of China's airline routes throughout 2018 is displayed in Figure 3. The number of airlines in the Chinese airline network sharply increased at 6:00 and suddenly decreased at 10:00. The primary operational time of the overall network was from 6:00 to 24:00, such that 99% of flights in 97% of airports occurred during this time period. Peaks in flights occurred at 07:00 and 10:00, with each displaying an average number of flights of 510 and 530, respectively. These peaks signify a limitation in the operational capacity of the overall civil aviation network. The network was weighed based on the number of flights in each time period to investigate the changes in flight schedules, resulting in similar findings to those of the unweighted network. Unlike urban transportation, air transportation experiences long periods of sustained peak traffic [34]. According to regulations of the Civil Aviation Administration, domestic airlines are advised to reduce the number of \"red-eye flights\", which are flights that depart and arrive after midnight. On average, there are fewer than 10 flights per day (0.1% of the total) that are scheduled to take off after midnight in the flight schedule, but in actual operations, an average of 94 flights per day (3% of the total) take off after midnight. To further explore this phenomenon, the authors analyzed the flight schedule by dividing time into hourly intervals based on scheduled departure time (Figure 4). The chart clearly shows that almost no flights are scheduled to take off after midnight in the Civil Aviation Administration's flight schedules. The researchers calculated the difference between the scheduled and actual number of flights for each hour of the year and found that there were discrepancies between 5:00 and 12:00 and between 15:00 and 16:00. This deviation led to flight delays and an increase in the number of \"red-eye flights\" in operation. However, during other times, the actual number of flights exceeded scheduled estimates, suggesting that airlines handled abnormal flights during those periods. This study evaluated representative airports of various types, including domestic slot-coordinated airports such as Beijing Capital International and Xi'an Xianyang International, gateway airports such as Urumqi Diwopu International and Kunming Changshui  
Figure 3: The presented graph depicts the temporal evolution of the number of airports and flight routes in the CATN. The yellow and green lines correspond to the average number of planned and actual flight routes per time period, whereas the purple and orange lines indicate the average number of planned and actual airports. The shaded regions of diverse colors illustrate the fluctuation of daily actual data around the mean value. International, and provincial airports such as Lanzhou Zhongchuan International. Through examining the number of flights over time (Figure 5), the authors identified significant peak periods of outbound flights for Beijing, Xi'an, and Kunming, with values that dropped noticeably after 10:00. This suggested ample capacity at the operations, airspace, runways, and other support resources that could redistribute flights via ground wait and flow control after 10:00. However, Urumqi and Lanzhou had stable values, implying that their support resources such as runways and airspace were nearing saturation. Figure 4: The presented figure showcases the changes in the hourly counts of airports and flights in the CATN. Specifically, the green and yellow lines correspond to the actual and planned average count of flights, respectively, for each time period. Equivalently, the purple and orange lines represent the actual and planned average count of airports, respectively, for each time period. Various shaded regions of divergent colors correspond to daily actual data that fluctuate around the mean. Figure 5: Flight volumes at specific airports over time.