# A Topological Sensitive Node Importance Evaluation Method in Aerospace Information Networks
## 5 Experimental Simulation and Analysis
### Simulation Experiment and Analysis of Node Importance
#### 5.1.1 Node Importance Algorithm Accuracy Evaluation  
On this basis, by comparing the four methods of degree centrality, natural connectivity, jumping-surface node method and mutual information method, the feasibility and effectiveness of the method in this paper are illustrated. Let us take Figure 4 as an example and compare the results of the five sorting methods in Table 3. Since the network is symmetrical, this article only lists some representative node evaluation results, as shown in the following Table.  
It can be seen from Table 3 that all methods can evaluate the importance of nodes. Degree centrality is the simplest measurement method, reflecting the importance of nodes in a local range. However, this method cannot distinguish the importance order of nodes, because some nodes have the same degree centrality value, for example, both nodes 2 and 4 are 0.2. We cannot compare other methods intuitively. Therefore, we delete some important nodes and the changes in network connectivity further clarify the performance of natural connectivity, the jump-surface node method, mutual information method and our method in this paper.  
Removing nodes from the network will reduce the connectivity of the network and the worst connectivity corresponds to the best sorting method. Connectivity is reflected in two  
Figure 4: Network topology (Numbers 1-15 represent satellite nodes at different altitudes) (time T1).  
Figure 5: Network topology (Numbers 1-15 represent satellite nodes at different altitudes) (time T2).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Degree Centricity**} & \multirow{2}{*}{**Natural Connectivity**} & \multicolumn{2}{c}{**Jump-Surface**} & \multicolumn{2}{c}{**Mutual Information**} & \multirow{2}{*}{**Our Method**} \\  & & & & **Node Method** & & & **Method** & \\ \hline \multirow{2}{*}{**Node**} & **Important Degree** & \multirow{2}{*}{**Node**} & **Important Degree** & \multirow{2}{*}{**Node**} & **Important Degree** & \multirow{2}{*}{**Node**} & **Important Degree** \\ \hline
2 & 0.2000 & 4 & 0.1436 & 2 & 0.2406 & 4 & 0.8109 & 2 & 0.2142 \\
4 & 0.2000 & 2 & 0.1202 & 4 & 0.2256 & 2 & 0.4054 & 1 & 0.1064 \\
1 & 0.1344 & 8 & 0.1012 & 1 & 0.1662 & 8 & \(-\)0.4055 & 4 & 0.0884 \\
8 & 0.1344 & 1 & 0.0742 & 8 & 0.1488 & 1 & \(-\)0.8109 & 8 & 0.0152 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Evaluation results of node importance in Figure 2.  
measures: the number of subgraphs and the size of the largest subgraph after decomposition. The larger the number of subgraphs or the smaller the size of subgraphs, the worse the connectivity, which means that the corresponding sorting method has better performance.  
We delete four nodes in the network separately, and the change in network connectivity is shown in Figure 6. We can see that when node 2 is deleted, three subgraphs are generated, therefore node 2 is the most important in the network. When nodes 1 and 4 are deleted, two subgraphs are generated. However, when node 1 is deleted, the size of the largest subgraph is smaller, therefore node 1 is more important than node 4. This conclusion is consistent with the method in this paper. These results show that the method in this paper has good performance in node importance evaluation.  
Spatial information network is characterized by high dynamic, its topology changes regularly in the cycle, and the structure changes very small. The algorithm proposed in this paper and the existing four node importance evaluation indexes (Degree centrality, Natural connectivity, Jump-surface node method, Mutual information method) are used to calculate the importance of each node in Figures 4 and 5. The experimental data are shown in Tables 4 and 5.  
In order to more intuitively observe the changes of node importance before and after the network topology changes, we compared the natural connectivity, mutual information method, degree centrality, jump-surface node method, and node importance evaluation results of our algorithm, as shown in Figure 7.