# A New BAT and PageRank Algorithm for Propagation Probability in Social Networks
## 1 Introduction
However, using this method will lead to a large number of spam links intentionally generated by people in order to increase the probability of the page. The TwitterRank algorithm assigns different propagation weights for Twitter users to track the similarity of different specific topics and web page structures, while the probability will vary with the posting rate of the post [27]. The PageRank algorithm is based on web page links; a page's PageRank value represents random clicks on the page as the probability distribution of reaching any particular node, and the source of its value is based on the PageRank values of all other pages linked to it [28]. This study adopts the PageRank algorithm originally used by Google to analyze the relevance and importance of web pages and uses the PageRank value to measure the importance of nodes to convert it into an appropriate propagation probability. However, studies in [29; 30; 31] pointed out that users of social networks have different topic preferences, resulting in different topics with different propagation effects. Therefore, in order to analyze the influence of different user preferences on propagation probability, this study also uses Personalized PageRank to measure the different node weights due to different node themes [32; 33; 34]. There are many methods which can be used to search for the propagation path of social networks. [PERSON] et al. proposed that the hierarchical structure can be inferred from the network and applied to solve the path prediction problem in social networks [35]. [PERSON] and [PERSON] proposed a prediction algorithm based on a supervised random propagation path; the random path is more convincing because the transfer probability between nodes is different. However, this has not been applied in practice because the model requires significant computing time [36]. Whether based on random paths or fully supervised, these methods are generally complex and difficult-to-understand and are more suitable for problems with a fixed number of sink nodes. However, the propagation process in the social networks studied in this work does not have a fixed sink node, so the propagation problem in social networks to be predicted in this study requires an easy-to-understand new method to predict its propagation path and propagation probability. This study adopts a binary-addition tree algorithm (BAT) to predict propagation in social networks [37]. BAT algorithms are similar to depth-first search (DFS) [38] and breadth-first search (BFS) [39] algorithms. However, BAT algorithms-in addition to being easy to understand and program, have the main advantage of flexibly in searching all propagation states in the binary network, which makes path exhaustion simpler and easier to change for different applications [37]. This study aims to propose a new method to calculate the probability of propagation areas in social networks and to quickly identify nodes in the network that require close attention. In addition to adopting the traditional PageRank algorithm and the Personalized PageRank algorithm, this study also proposes a novel state concept and a new method based on the combination of a BAT algorithm and the PageRank algorithm to predict the area and probability of possible impacts of propagation in the modeled social network and perform social network analysis (SNA). Hence, the manuscript's value is emphasized in following list:  
1. Firstly, we prove that the social network is a scale-free network and use the Barabasi-Albert model to construct a prediction model. 2. After enumerating all possible propagation states through the BAT algorithm, the PageRank algorithm is used to calculate the occurrence probability and propagation probability of each social network node, and the Personalized PageRank algorithm is used to meet the user's preference. 3. Finally, a new BAT algorithm is used to calculate the probability prediction values of all nodes to different propagation ranges. 4.