## 6 Results and Analysis
### Impact of Network Parameters on Involnerability  
Figure 2 depicts the difference in invulnerability under three attack strategies with varied \(e\%\). For different \(e\%\), the invulnerability of the three attacks reaches the maximum when the number of communication rounds is 101. At this point, the descending sorting of invulnerability is maximum-degree attack, maximum-betweenness attack, and random attack. Moreover, under the case of \(e\%=10\%\), \(15\%\), \(20\%\), and \(25\%\), respectively, and the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(E\) & 0.5 J \\ \(E\)\(\&\) & 50 nJ/bits \\ \(efs\) & 10 pJ\(\cdot\)bit\({}^{-1}\)\(\cdot\)m\({}^{-2}\) \\ \(emp\) & 0.0013 pJ\(\cdot\)bit\({}^{-1}\)\(\cdot\)m\({}^{-4}\) \\ \(Eaggr\) & 5 nJ/(bit/message) \\ Coordinates of the BS & (0,0) \\ \(k\) & 4000 \\ \(N\) & 1000 \\ \(e\%\) & 10\% \\ \(r\) & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Initial setting of simulation parameters. number of communication rounds equals 400, the order of invulnerability for the three attack modes remains identical. In contrast, at \(e\%\) = 5%, the invulnerability of maximum-betweenness attack (0.350 J) is the largest and that of random attack (0.313 J) is the least. Figure 3 demonstrates the changes in invulnerability under three attacks with varying \(k\). The invulnerability subjected to these three attacks reaches the maximum at the same number of communication rounds (101). In comparing the maximum invulnerability, it is easy to observe that the invulnerability of the maximum-degree attack is the highest, while that of the random attack is the lowest. In particular, the greatest invulnerability (0.995 J) of the maximum-degree attack is the most remarkable for \(k\) = 6000. In the circumstance that the number of communication rounds is 400, at \(k\) = 2000, the invulnerability of maximum-degree attack substantially surpasses that of random attack (64.19%); at \(k\) = 5000, the invulnerability of maximum-degree attack is superior to that of maximum-betweenness attack and the invulnerability of maximum attack is 23.89% larger than that of random attack. Figure 3: Effects of changing \(k\) on invulnerability for varied attacks. Figure 2: Relationships between differing \(e\) and invulnerability under distinct attacks. Figure 4 shows the shifts in invulnerability under three attacks with various \(r\). When \(r\) is 1, 3, 4, and 5, the invulnerability of the three attacks simultaneously attains the maximum at 21, 61, 81, and 101 communication rounds, respectively. At \(r=2\), the invulnerability of random attack arrives at the peak value when the number of communication rounds is 21. Furthermore, the invulnerability of maximum-degree and maximum-betweenness attacks reaches the greatest value at 41 rounds. In the condition that \(r\) is 2, 3, and 5, it is obviously found that the invulnerability of the maximum-degree attack is the most satisfactory. At the same time, when \(r\) is 1 and 4, it is easily discovered that the maximum-betweenness attack has the most excellent invulnerability, but the random attack has the lowest invulnerability in both cases. In addition, in the case that \(r\) is 2, 3, 4, and 5, the invulnerability of maximum-degree attack is the most outstanding, and that of random attack is the most inferior; at \(r=1\), the invulnerability of maximum-betweenness attack is more heightened than that of maximum-degree attack and random attack. Figure 5 exhibits network invulnerability changes with different \(N\) for the three attacks. At 101 rounds, it can be uncovered that the highest invulnerability of maximum-degree, maximum-betweenness, and random attacks is ranked from high to low. For \(N=1200\), the most prominent invulnerability (0.997 J) of maximum attack is the highest. Moreover, when \(N\) is 1200 and 1000, the utmost invulnerability of maximum-betweenness attack is 0.990 J and 0.733 J, respectively, and the former is 35.06% higher than the latter.