# A Study on the Normalized Delineation of Airspace Sectors Based on Flight Conflict Dynamics
## 3 Idle/Busy Time Segmentation
### Selection of Assessment Indicators  
In order to comprehensively assess and classify the air traffic operation posture, six complex network characteristic indicators that can reflect the characteristics of the airspace conflict network from multiple perspectives are selected to describe the flight posture. 1. Total Node Degree Degree is a key attribute of a node that indicates the number of links between that node and other nodes. In a conflict network, the degree value reflects the number of conflicts between one aircraft and other aircraft, and most intuitively reflects the local conflict situation, denoted by \(k_{i}\): \[k_{i}=\sum_{j=1}^{N}a_{ij}\] (7)  
\(k_{i}\) is the degree value of node \(i\), \(N\) is the total number of nodes in the network, \(a_{ij}\) denotes the connectivity of two nodes, \(a_{ij}=1\) if connected and \(a_{ij}=0\) otherwise. The total node degree reflects the total number of conflicts in the network; \(k_{sum}\) is denoted by:  
\[k_{sum}=\sum_{i=1}^{N}k_{i} \tag{8}\]  
2. Average Node Degree  
On the basis of the degree value, for networks, the average degree is an important attribute of the network, indicating the average number of links between each node and other nodes throughout the network. In a conflict network, the average degree value can reflect the average number of conflicts each aircraft forms with its surrounding aircraft, denoted by \(\overline{k}\):  
\[\overline{k}=\frac{1}{N}\sum_{i=1}^{N}k_{i} \tag{9}\]  
3. Average Point Intensity  
Point strength is the expression of the degree value after weighting; the index can not only reflect the number of neighboring nodes, but also reflect the degree of influence on the node around the node. In the conflict network, the average point strength can reflect the urgency of the conflict, and indirectly represents the average pressure of control deployment, which is denoted by \(\overline{s}\):  
\[\overline{s}=\frac{1}{N}\sum_{i=1}^{N}\sum_{j=1}^{N}a_{ij}\omega_{ij} \tag{10}\]  
\(a_{ij}\) is the connection relationship between two nodes, \(a_{ij}=1\) if connected, \(a_{ij}=0\) otherwise; \(\omega_{ij}\) is the edge right between nodes \(i\), \(j\). 4. Average Weighted Aggregation Factor \(\overline{C}\)  
The weighted aggregation coefficient is a weighted expression of the ordinary aggregation coefficient, and a single value indicates the degree of aggregation at the location of anode and the degree of proximity between nodes, while the average weighted aggregation coefficient can reflect the degree of aggregation of the whole network. In a conflict network, this value can describe the degree of conflict aggregation of the network as a whole, which is denoted by \(\overline{C}\):  
\[\overline{C}=\frac{1}{N}{\sum\limits_{i=1}^{N}{c(i)}} \tag{11}\]  
\(C_{i}\) is the weighted aggregation factor, calculated as follows:  
\[C_{i}=\frac{1}{(k_{i}-1)s_{i}}{\sum\limits_{m,n}{\frac{\omega_{im}+\omega_{in} }{2}\Delta_{abc}}} \tag{12}\]  
\(k_{i}\) is the degree of node \(i\); \(s_{i}\) is the point strength of node \(i\); \(\Delta_{abc}\) is the number of connected triples; \(m\), \(n\) are the neighbor nodes of node \(i\). 5. Network Density  
In the flight conflict network, the network density can be used to describe the denseness of the interconnecting edges between the nodes in the network, and the value can reflect the degree of saturation to the flight posture, denoted by \(ND\):  
\[ND=\frac{2L}{N(N-1)} \tag{13}\]  
\(L\) is the actual number of connected edges in the network. 6. Network Efficiency  
The network efficiency visualizes the connectivity of the entire network; the efficiency between two nodes is expressed as the reciprocal of the distance to each other, while the efficiency of the entire network is the average of the efficiencies between every two pairs of nodes. In the conflict network, this value can easily represent the spreading breadth of the aircraft conflict, defined as:  
\[NE=\frac{1}{n(n+1)}{\sum\limits_{i\
eq j}{1/d_{ij}}} \tag{14}\]  
\(d_{ij}\) is the shortest path between two nodes \(i\), \(j\).