# A New BAT and PageRank Algorithm for Propagation Probability in Social Networks
## 4 Simulation Experiment
### Results and Discussion
#### 4.2.3 Personalization Vectors and Propagation Probability  
In the propagation process of social network, the authority, professionalism, trust and influence of propagation nodes are all related to user preferences, but most influence studies of social networks largely ignore this [31]. In this study, the personalized vector in the Personalized PageRank algorithm is used to intervene in the random viewers in the PageRank algorithm to prefer a specific node in the random walk process so as to increase the distribution weight of the node to represent the user's preference node or relevance of information propagation.  
In Case 2, in which node 3 was originally the node with the highest number of adjacent nodes and the highest PageRank value, we set random viewers to prefer a specific node 3 in the random walk process. From Table 11, it can be found that when the personalized vector \(r_{3}=1\) of node 3, \(PPR(3)=0.3438\) is higher than the original \(PR(3)=0.2372\). However, in the \(R_{2}\)-\(R_{1}\) column in Table 14, it can be found that most of the propagation probabilities increase, while the propagation probability of node 3 decreases. The reason for this is that node 3 connects most of the nodes, resulting in it affecting the PageRank value of maximum propagation state of other nodes, causing them to also increase when the PageRank value of node 3 increases, as shown in Table 16.  
\begin{table}
\begin{tabular}{c} **Case 3** \\ \(PPR_{max}\)**(\(i\))** \\ \end{tabular} & **Ranking** \\ \hline
0 & 0.3626 & 7 & 0.4526 & 6 & 0.3191 & 8 \\
1 & 0.3990 & 4 & 0.4859 & 4 & 0.4203 & 3 \\
2 & 0.4512 & 3 & 0.5162 & 3 & 0.3807 & 5 \\
3 & 0.6367 & 1 & 0.5633 & 2 & 0.6762 & 1 \\
4 & 0.3990 & 4 & 0.4859 & 4 & 0.4203 & 3 \\
5 & 0.5368 & 2 & 0.5945 & 1 & 0.6189 & 2 \\
6 & 0.3633 & 6 & 0.4367 & 7 & 0.3238 & 7 \\
7 & 0.3753 & 8 & 0.3260 & 8 & 0.3242 & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Ranking for PageRank value of maximum propagation state nodes.  
In Case 3, in which node 1 was originally the node with the lowest number of adjacent nodes and the lowest PageRank value, we set random viewers to prefer a specific node 1 in the random walk process. When the PageRank value of node 1 increases, it affects the PageRank value of maximum propagation state of other nodes. However, because there are not many nodes connected to node 1, the PageRank value of maximum propagation state does not increase much. As shown in Table 17, the number of nodes with increased propagation probability is small. From the \(R_{3}\)-\(R_{1}\) column in Table 14, it can be found that most of the propagation probabilities decrease, which means that increasing the personalized vector of nodes with fewer connections has no obvious effect on the propagation probability of nodes.  
When we bias the random viewers to the nodes with more adjacent nodes in the random walk process, the propagation probability of more nodes can be increased. However, increasing the distribution weight of nodes with fewer adjacent nodes does not have much influence. Therefore, it is assumed that an advertiser plans to place an advertisement and that there are two nodes with the same theme. If a node with a higher number of adjacent nodes is selected, it relatively increases the probability of propagating more pages.