# A Topological Sensitive Node Importance Evaluation Method in Aerospace Information Networks
## 3 Node Importance Evaluation Model
### Node Importance Transfer Probability Matrix  
If any node in the spatial information network is isolated, it will inevitably be affected and restricted by adjacent nodes. The interaction between nodes can be described by the probability transfer matrix based on node importance [27]. There are complex dependencies between nodes and the dependence intensity varies with the location of the nodes. For node \(i\), we define its adjacent nodes as the first layer nodes and the nodes with a distance of 2 as the second layer nodes, and so on. Since the importance of node \(i\) in the nodes of the same layer is different and the node degree centrality can be used to describe the direct influence of a node in the network, we use the degree centrality to describe the dependence between nodes. The following experiment will show the influence of a node on other nodes. Figure 1 is a typical complex network topology diagram with nine nodes. Node 4 is directly connected to nodes 3-7 and they are all located on the first layer of node 4. We use natural connectivity to calculate the importance of each node. Table 1 shows the changes in the importance of nodes 3-7 before and after deleting node 4. We can see that although nodes 3-7 are directly connected to node 4, when node 4 fails, the difference in the impact on its adjacent nodes varies, indicating that the contribution of nodes to nodes at different positions on the same layer is different. Therefore, if there is a \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Node** & **Node 3** & **Node 4** & **Node 5** & **Node 6** & **Node 7** \\ \hline Before deleting & & & & & \\ node 4 & 0.357 & 0.697 & 0.254 & 0.525 & 0.083 \\ After removing & & & & & \\ node 4 & 0.238 & / & 0.099 & 0.345 & 0 \\ Difference & 0.118 & / & 0.155 & 0.180 & 0.083 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Changes in importance before and after deleting node 4. Figure 1: Network topology (Numbers 1–9 represent node numbers in complex networks). strong dependency between a node and another node, the importance of the node can be transferred to another node. The impact of a node failure is not limited to its adjacent nods. Take node 2 in Figure 1 as an example, we can see that node 1 is on the first layer of node 2, and node 4 is on the second layer of node 2. We delete node 1 and node 4 and observe how it affects node 2. The experimental results are shown in Table 2.  
It can be seen from Table 2 that when node 1 fails, the impact value on node 2 is 0.065, and when node 4 fails, the impact on node 2 is 0.095. It can be seen that the influence of node 4 on node 2 is higher than that of node 1 on node 2. The experiment shows that when the nodes have strong reachability, it does not only affect the adjacent nodes but also affects the non-adjacent nodes. For a node, if the influence of non-adjacent nodes is greater than that of adjacent nodes, the importance of non-adjacent nodes cannot be ignored. However, if multi-step non-adjacent nodes are considered, the complexity of the algorithm will increase. Achieving a balance between running speed and accuracy is the key to the problem. Reference [28] found that when considering non-adjacent nodes of order two or above, the accuracy improvement is marginal but the efficiency of the algorithm drops sharply. Therefore, considering the adjacent nodes in the second order can balance the accuracy and time complexity and this paper only considers the second-order neighbors when evaluating the importance of nodes. Next, we will characterize the importance of dependence between the nodes in the network. In Figure 1, it is not difficult to identify when node 4 is deleted, nodes 7-9 will become isolated nodes, and their importance is 0. However, nodes 3, 5 and 6 are adjacent to other nodes, and their importance will be different and will not be 0. Therefore, if the degree of a node is smaller, it is more easily affected by other nodes.