# An Attention-Based Deep Convolution Network for Mining Airport Delay Propagation Causality
## 4 Case Study
### Topological Property Analysis
Figure 18a shows the relationship between the average daily departure flight volume and degree, that is, the delay caused by airports with different flight volumes is affected by how many airports are delayed and how many airports are affected by delays. There are 6 airports with a small number of flights, but the out-degree is greater than 25. There are 8 airports with a large number of flights, but the in-degree and out-degree are small. In general, most airports have 0-300 departure flights, and 0-10 inbound and outbound flights. These airports are susceptible to being influenced by other airports, and at the same time, they are also easily influenced by other airports. Airports with more than 300 flights have small in-degrees and are not easily affected by other airports. They have a strong ability to absorb delays. From here, it can also be seen that the airport with the smallest number of flights has the largest in-degree and out-degree. Figure 18b shows the relationship between the average delay of departure and the degree value for each airport. The relationship between airport delay level and out-degree value is similar to the relationship between airport flight volume and out-degree value. The smaller the average delay time, the easier it is to affect other airports. There is no obvious relationship between the in-degree and the average delay time of the airport. It does not mean that the airport with a smaller delay is more easily affected by other airports, and it does not mean that the airport with greater delay is more easily affected by other airports. Figure 17: Relationship between airport in-degree and out-degree. Figure 18: Relationship between 20 degrees and departure flight volume and average delay time. (**a**) Degree value vs average daily departures, (**b**) Degree value vs average daily. Table 2 gives the values of connection density, interaction parameter, aggregation coefficient, and connection density \(l_{d}\) to represent the degree of tightness of network connection, which is defined as the ratio of the number of edges of the network to the number of possible edges of all nodes, and the value range is between [0, 1]. The larger the value of \(l_{d}\), the tighter the network connection is, and the more easily the delay propagates in the network. The connection density of this causal relationship network is 0.0266, which is related to the choice of model parameters so that the network connection is not tight, and the delay propagation can be blocked by certain measures in the airport network. The interaction parameter indicates whether the delay propagation between airport pairs is bidirectional. Delays at the airport \(i\) will affect delays at airport \(j\), and delays at airport \(j\) will also affect delays at the airport \(i\). The interaction parameters were calculated using the method provided in [31]. The average \(\overline{R}\) of 1000 random networks with the same number of nodes and edges generated by the network randomization technique is 0.17. Compared with this value, the interaction parameter of the causal network is much smaller than \(\overline{R}\), so the number of airport pairs in the network where delays propagate and influence each other is considered to be very small. If the delay of one airport leads to the delay of other airports, then other airports are called neighbor airports. The ratio of the actual causal relationship between these neighboring airports and the possible causal relationship is called the aggregation coefficient, which reflects the aggregation degree of the airport. For directed networks, the clustering coefficient is calculated using the method provided in [17,19]. The overall clustering coefficient of this causal network is 0.1405, which is larger than that of the random network (0.092). It shows the clustering trend among airports in the delay causality network, and delay causality often exists between the other two airports affected by the delay of one airport.