# A New BAT and PageRank Algorithm for Propagation Probability in Social Networks
## 1 Introduction  
With the commercial effect of viral marketing and word-of-mouth marketing, social networks are regarded as a medium for propagating information, ideas and influence between nodes [1; 2; 3; 4]. The propagated influence of information propagation in social networks, which use the behavior of user information propagation in social networks to evaluate propagated influence and find the key nodes in order to achieve the greatest influence on social networks during the propagation of these nodes [1; 5], is a hot research area [1; 6; 7; 8; 9]. In other words, investors focus on the high connectivity and high propagation of social networks and accurately invest information in the source nodes of propagation rather than invest many resources in many nodes. The use of social network propagation achieves the purpose of information propagation, which is also an advantage of social networks [10]. In fact, people's lives and sources of information are largely affected by social networks [11], so understanding how information propagates within social networks is crucial for designing effective promotion strategies and preventing the propagation of malicious information. It is found social networks are scale-free networks in the real world [12; 13], and the degree distribution of scale-free networks follows the power law distribution [14]. Many practical and important networks--such as the World Wide Web, power grids,etc.--are scale-free networks, which share information between nodes in the network through network connections [14; 15]. In the era of social networking, such networks have both flaws and virtues [16]. The benefits include the rapid transmission of information [16] and the development of e-commerce platforms [17], interpersonal relationships [17], etc., while there are also many disadvantages, such as internet viruses [18], rumors [19], etc. The effective promotion of policies, placement of commercial advertisements and prevention of the spread of malicious information in social networks are important topics in social network analysis. For example, if a node with a high probability of spreading is identified when the expected spread is large, better spread can be achieved by placing advertisements on this node. On the contrary, when misinformation spreads among social networks, identifying nodes with a higher probability of spreading in the early stage of dissemination can effectively prevent the dissemination of information in a timely and effective manner. By predicting the source node with the best communication ability in the social network, providing them with information and asking them to use their own influence to publicize that information, a series of communication effects can be triggered. Therefore, the motivation of this research is to propose a new method for the prediction and modeling of a social network's propagation probability so as to quickly determine the nodes with greater propagation influence in social networks and their propagation probabilities. In addition, the personalization vector in the Personalized PageRank is used to adjust the distribution of node propagation probability in the network, and the influence of user preference on the propagation probability is analyzed. Much research has been devoted to modeling the propagation process in social networks [20; 21; 22; 23; 24]. Among the different models of scale-free networks, the Barabasi-Albert model proposed by [PERSON] and [PERSON] is more common and has many applications [15]. Therefore, this study adopts the Barabasi-Albert model to simulate propagation in social networks and generate test data to verify the performance of the proposed algorithm. The method of measuring the probability of propagation in social networks will vary depending on the focus of research. The most intuitive method is to use the number of node connections with a high probability of page appearance when the number of node connections is large, which is called in-degree [25; 26].