### Theoretical Framework
#### 3.3.1 Node Influence Calculation  
In social research, based on the understanding if strong and weak relationships between users, nodes in a social network play various roles. The positions of different nodes in the network topology vary, and their functions differ accordingly. Currently, many methods are available to describe the positional attributes of nodes in the network. PageRank is a method that measures the importance of a node based on the directionality of edges, treating the directed edges in a graph as a form of endorsement. This allows for the calculation of the value or importance of each node in a directed graph. PageRank effectively illustrates a real-world scenario; when users have more connections, they tend to exert greater influence within their community. By leveraging the characteristics of the PageRank algorithm, the impact of users within a network can be measured. Therefore, this study primarily uses the PageRank value to measure a user's influence at the individual level. The PageRank calculation is shown in Equation (8):  
\[PR(i)=\frac{1-\alpha}{N}+\alpha\sum_{y_{j}\in N_{i}}\frac{PR(j)}{\text{Num}(N_ {i})} \tag{8}\]  
where \(\text{Num}(N_{i})\) represents the number of users in set \(N_{i}\) and \(N\) represents the total number of users in the network. The parameter \(\alpha\), which is usually set to 0.85 [48], is a damping factor in the PageRank algorithm. A PageRank calculation example is shown in Figure 7 to calculate the PageRank value of node \(C\). The iterative process for this calculation is depicted in Figure 8.  
* Initialization: Assign an initial value of 1 to all nodes in the network. * Identify Influence: Determine which nodes influence node \(C\). From the directed connections between the nodes, it can be seen that node \(C\) receives influence from nodes \(B\) and \(E\), making node \(C\) a follower of \(B\) and \(E\). During information propagation, node \(C\) is influenced by nodes \(B\) and \(E\). As shown in Figure 7, node \(B\) influences nodes  
Figure 6: Frame diagram based on the user influence information dissemination model. Figure 7: User link diagram. \(A\), \(C\), and \(D\), meaning node \(C\) receives an influence of \(\frac{PR(B)}{3}\) from \(B\). Similarly, nodes \(A\) and \(D\) also receive \(\frac{PR(B)}{3}\) from \(B\). Likewise, node \(C\) receives an influence of \(\frac{PR(E)}{4}\) from \(E\). * Calculate PageRank for node \(C\): Based on the directed relationships in the network, node \(C\) is influenced by nodes \(B\) and \(E\), meaning \(PR(C)=\frac{PR(B)}{3}+\frac{PR(E)}{4}\). However, there is a certain probability that node \(C\) does not receive influence from \(B\) and \(E\) but, instead, randomly receives information from the entire network. The probability of receiving information from \(B\) and \(E\) is defined by \(\alpha\), and the PageRank formula for node \(C\) is expressed as \[PR(C)=\frac{1-\alpha}{7}+\alpha\Big{(}\frac{PR(B)}{3}+\frac{PR(E)}{4}\Big{)}\] (9)
* Iterate: Repeat the above steps iteratively until the results converge. When considering information dissemination, structural hole nodes are often overlooked. As shown in Figure 9, both nodes A and B occupy critical positions in the network. Node A is located at the center of a closely connected community, while node B is situated at the intersection of multiple communities, representing a structural hole. Node A exhibits a high degree of connectivity with its neighbors, and it has high centrality in the network topology. According to triadic closure and sociological theories, nodes with high connectivity often hold some degree of authority. In information dissemination, nodes with high centrality are typically regarded as key nodes, whereas structural hole nodes on the periphery are often ignored. In Figure 9, although node B is less connected to its neighbors, it benefits from its cross-community position.