## 2 Route Network Construction
### Determination of Route Network Margins  
On the basis of the contiguous relationship, four indicators, namely, route saturation, flight delay rate, meteorological conditions, and military aviation activities, were analyzed, as shown in Table 1.  
According to the influencing factors of the four indicators in Table 1, the corresponding contiguous weights were calculated by the hierarchical analysis process (AHP). The 1-9 scale method shown in Table 2 is a common method of comparing indicators. Through expert assessment, the four indicators can be considered to be ranked in order of importance as AS > DF > WC > MA. Matrix \(S\) describes the results of the comparison between the four indicators, as follows:  
\[S= \begin{bmatrix}1&3&5&7\\ 1/3&1&3&5\\ 1/5&1/3&1&3\\ 1/7&1/5&1/3&1\end{bmatrix}  \tag{1}\]  
Calculate the eigenvector \(\omega\) corresponding to the largest eigenroot \(\lambda\) of the judgment matrix \(S\) and normalize it to obtain the weight vector \(W\):  
\[W_{i}=\sqrt[n]{\prod_{j=1}^{n}a_{ij}}\bigg{/}\sum_{i=1}^{n}\sqrt[n]{\prod_{j=1 }^{n}a_{ij}} \tag{2}\] \begin{table}
\begin{tabular}{c c c} \hline
**Index** & **Method** & **Influence Degree** \\ \hline Airline saturation (AS) & The ratio of the route flow to the maximum capacity of the route. & The higher the route saturation, the greater the weight of the network edge, and the more likely it is to affect the corresponding two nodes. \\ Delay rate of flight (DF) & The ratio of the delayed flights to the connecting airport and navigation points on that day. & The higher the delay sorting ratio, the less the impact on the network, and the smaller the weight value. \\ Weather conditions (WC) & Weather conditions on the route on the same day. & The worse the meteorological conditions, the greater the weight of the network connection edge, and the more likely to cause the impact. \\ Military navigation activities (MA) & The ratio of the time of military navigation affecting the operation of the route to the total time of normal operation. & The more military aviation activities, the greater the potential conflict, and the greater the impact on the network delay. \\ \hline \end{tabular}
\end{table} 
Table 1: Main influencing factors. \begin{table}
\begin{tabular}{c c} \hline
**Factor i Compared to Factor j** & **Scale \(S_{ij}\)** \\ Equal Importance & 1 \\ Marginally Important & 3 \\ More Important & 5 \\ Very Important & 7 \\ \hline \end{tabular}
\end{table} 
Table 2: Scale and description. Where \(a_{ij}\) is the element in matrix A and \(W=[W_{1},W_{2},\cdots,W_{n}]^{T}\) is the eigenvector corresponding to the largest eigenvalue of matrix \(S\). According to Equation (2), the weight vector is calculated as follows:  
\[W=[W_{1}W_{2}W_{3}W_{4}]=[0.56500.26220.11750.0553] \tag{3}\]  
Next performs a consistency test and calculates the largest eigenvalue: \(\lambda_{\text{max}}\)  
\[\lambda_{\text{max}}=\frac{1}{n}\sum_{i=1}^{n}\frac{\sum_{j=1}^{n}a_{ij}W_{j}}{ W_{i}}=4.1169 \tag{4}\]  
Coherence indicator CI reads. \[CI=\frac{\lambda_{\text{max}}-n}{n-1}=0.0389 \tag{5}\]  
Consistency weighting CR is. \[CR=\frac{(\lambda_{\text{max}}-n)/(n-1)}{RI}=0.0438 \tag{6}\]  
Where, \(RI\) is the random consistency indicator, when \(n=4\), \(RI\) is taken as 0.9. Therefore, the judgment matrix satisfies the consistency test and the weights of the indicators are as follows:  
\[W_{AS}=0.5650,\ W_{DF}=0.2622,\ W_{WC}=0.1175,\ W_{MA}=0.0553\]  
Due to the differences in the order of magnitude of each data, the maximum-minimum method was used to normalize each indicator. The route saturation AS was processed as in Equation (7).