## 3 Proposed Method  
### Information Diffusion Model  
In this section, we first specify the definition of the research and then introduce the model, where we focus on three major details: information perception, information evaluation, and information transmission. **Definition 1**. : _An online social network with \(N\) users can be represented by a graph \(G(V,E,C)\), Set of nodes \(V\) denotes users, where \(|V|=N\) and the set of edges \(E\) specifies the relationship between users. \(C\) is a set of individuals' characteristics, where \(\forall c_{i}\in C\) ; \(c_{i}\) identifies the characteristics of the individual \(v_{i}\)._  
**Definition 2**. : _The state of the nodes on the online social networks is denoted by the set \(S\), where \(\forall s_{i}\in S\), \(s_{i}\) represents the state of node \(v_{i}\)._  
**Definition 3**. : _The information diffusion process is a sequence of \(G\) based on time \(P=\{P_{1},P_{2},P_{3}\cdots P_{t}\}\), where \(P_{t}=(G,S_{t})\). \(S_{t}\) specifies the state of all nodes on an OSN at time \(t\)._  
After in-depth analysis of the information diffusion process from one node to another on OSNs, we divide the process into three parts, as shown in Figure 3.  
Figure 2: Explosion shock wave overpressure decays with time. Information perception explains how each node on the OSNs receives information. Individuals can receive a wide variety of information released by neighbors. The individual will decide whether to receive based on the closeness of the relationship between the sender and the receiver. Information evaluation formulates how the node evaluates the information. The individual chooses his own state (such as knowing, like, comment, forwarding, etc.) based on the evaluation result and the state of neighbors. After the individual is activated, the state may continue to change over time. Information transmission defines how the information received by each node is transmitted to other nodes. This part defines the transmission rules of information. We assume that the higher attractiveness of the information, the larger probability of forwarding by individuals. In the following, we describe in detail the specific definitions of these three components in our model. Before analyzing in-depth the information diffusion process on OSNs, we were inspired by the explosion shock wave model in physics. The process of information diffusion is similar to the explosion of an information bomb. The influence of the information spreads outward from the source and decays with the propagation distance. The influence of the information is initially large, and then gradually decreases after the individual is affected. Similarly, the peak of the shock wave overpressure decays with distance, and the overpressure at a certain point in space decays with time. In this case, the value of information represents the equivalent of explosive \(W\). The greater the value of the information, the stronger the influence will be. The length of time under positive pressure \(T^{+}\) indicates the forgetting time of an individual. The decay coefficient \(\alpha\) represents the degree of aversion information. Since distance is proportional to time, \(r\propto t\), we assume \(r=0.6+0.01*t\). According to Formulas (1) and (2), we define the value of information influence received by an individual as follows:  
\[I_{i}^{+}=\left\{ \begin{array}{c}\frac{1.4071}{Z}+\frac{0.554}{Z}-\frac{0.03 57}{Z^{3}}+\frac{0.000625}{Z^{4}}\ (0.1\leq Z\leq 0.3)\\ \frac{0.619}{Z}+\frac{0.033}{Z^{2}}+\frac{0.213}{Z^{3}}\ (0.3\leq Z\leq 1)\\ \frac{0.066}{Z}+\frac{0.045}{Z^{2}}+\frac{0.329}{Z^{3}}\ (1\leq Z\leq 10) \end{array} \right. \tag{4}\]  
\[I_{i}(t)=I_{i}^{+}(1-\frac{t}{T^{+}})e^{-\alpha_{i}t} \tag{5}\]  
\(I_{i}^{+}\) represents the maximum influence of information on node \(v_{i}\) and \(t\) is the time point when the node \(v_{i}\) is activated.