Complex networks have encouraged scholars to develop an effective method for abstracting and optimizing aviation networks. However, researchers often overlook the aviation network’s temporal attribute and treat it as a static network. Aviation networks have strong temporal characteristics and the dynamic connection cannot be realistically described by a static network. It is necessary to more accurately and realistically represent these connections during the operation of an aviation network. This study explored temporal structures of the Chinese aviation temporal network (CATN) based on flight schedules and actual operational time data. Temporal networks based on time windows were represented to analyze the temporal topology features and robustness of the CATN. The results demonstrated the following: (1) based on the spatial-temporal aviation network, there is a morning departure peak (7:00–8:00) and an evening arrival peak at the airline hub (20:00–21:00); (2) examining the centrality of each airport in the CATN at various time intervals exposed fluctuations in their rankings, which could not be identified by a static network, and (3) the robustness of the CATN was found to be unaffected by time windows, but it displayed poor resilience against deliberate attacks, particularly when subjected to betweenness and closeness attacks, which target the network’s shortest paths. For obtaining a greater understanding of the operating situation of civil aviation, displaying the topological features and robustness of the temporal network is of great importance.

Kuiper's statistic is a good measure for the difference of ideal distribution and empirical distribution in the goodness-of-fit test. However, it is a challenging problem to solve the critical value and upper tail quantile, or simply Kuiper pair, of Kuiper's statistics due to the difficulties of solving the nonlinear equation and reasonable approximation of infinite series. In this work, the contributions lie in three perspectives: firstly, the second order approximation for the infinite series of the cumulative distribution of the critical value is used to achieve higher precision; secondly, the principles and fixed-point algorithms for solving the Kuiper pair are presented with details; finally, finally, a mistake about the critical value $c_n^{\alpha }$ for $(\alpha ,n)=(0.01,30)$ in Kuiper's distribution table has been labeled and corrected where n is the sample capacity and α is the upper tail quantile. The algorithms are verified and validated by comparing with the table provided by Kuiper. The methods and algorithms proposed are enlightening and worth of introducing to the college students, computer programmers, engineers, experimental psychologists and so on.

Air traffic controllers benefit from referencing historical dates with similar complex air traffic conditions to identify potential management measures and their effects, which is critical for understanding air transportation system laws and optimizing decisions. This study conducted data mining using flight timetables. It first explored airport congestion mechanisms and quantified congestion as time series, then proposed a higher-order cumulants based time series feature extraction method. This method was fused with other features to build a high-dimensional airport congestion feature vector, and finally K-means clustering was applied to extract and analyze congestion patterns. The clustering method was empirically validated with 2023 flight data from Guangzhou Baiyun International Airport and it accurately classified airport operational states. To verify universality, the same framework was applied to 6 airports under the "one-city, two-airports" layout in Beijing, Shanghai and Chengdu. Results showed significant congestion pattern differences between existing and newly constructed airports. Conclusions confirm the proposed feature extraction and clustering framework is effective and universal, and it can accurately capture airport congestion dynamics. Under the "one-city, two-airports" layout, existing and newly constructed airports differ significantly in operational modes, and most single-airport city airports have operational modes highly consistent with existing airports. This study provides valuable decision-making references for airport managers and air traffic controllers. It helps them deepen understanding of air traffic dynamics and airport congestion patterns, thereby optimizing traffic management strategies and improving airport operational efficiency.