### Theoretical Framework
#### 3.3.1 Node Influence Calculation
Within the same network topology, considering two time steps, node B, situated in the structural hole, has a broader reach and influences more users at \(t=2\) compared to highly central node A. Therefore, the influence of node B in information propagation cannot be overlooked. In this study, constraint is used as a metric to quantify the structural hole's influence. When assessing a node's propagation influence in social networks, both the intrinsic properties of the node and the external environment must be considered. Figure 8: Iterative PageRank process. In this study, the network constraint coefficient (\(C_{s}(v)\)) is defined, which is calculated using Equation (10). \[C_{s}(v)=\sum_{w\in\tau(v)}\left(p_{vw}+\sum_{q\
eq v,w}p_{vq}p_{qw}\right)^{2} \tag{10}\]  
\[p_{vw}=\frac{z_{vw}}{\sum_{w\in\tau(v)}z_{vw}} \tag{11}\]  
\[z_{vw}=\left\{ \begin{array}{ll}1,&\text{if there is a direct connection between nodes $v$ and $w$}\\ 0,&\text{otherwise}\end{array} \right. \tag{12}\]  
In this case, set \(\tau(v)\) represents the neighbors of node \(v\), and \(p_{vw}\) indicates the proportion of the relationship between nodes \(v\) and \(w\) relative to all of node \(v\)'s neighbor relationships[]. The calculations for \(p_{vq}\) and \(p_{qw}\) follow the same logic, representing the proportion of neighbor relationships between nodes \(v\), \(q\), and \(w\). If the value of \(C_{s}(v)\) is smaller, the node experiences less constraint in occupying a structural hole and is more likely to influence information dissemination. Therefore, a node's influence should be inversely proportional to its constraint (\(C_{s}(v)\)). The local clustering coefficient is another important factor used to measure the local influence of a node. The clustering coefficient reflects the degree of cohesion around a node, describing the tightness within a local range. It represents how closely knit a group is. A group with high cohesion often exhibits greater internal trust, making it easier for members to reach a consensus. In this paper, a node with a high clustering coefficient is considered a key authority in the local network topology and an important influential user in the information dissemination process. The calculation method is expressed as follows:  
\[C_{i}=\frac{t_{i}}{\frac{1}{2}\cdot d_{i}\cdot(d_{i}-1)}=\frac{2\cdot t_{i}}{d_ {i}\cdot(d_{i}-1)} \tag{13}\]  
where \(t_{i}\) represents the number of triangles involving node \(i\) and \(d_{i}\) is the degree of node \(i\). A higher clustering coefficient indicates a stronger local network presence, meaning the node plays a more influential role in its neighborhood. The positional features of nodes from various perspectives is comprehensively considered, selecting appropriate metrics and integration methods to assess the influence of nodes in a social network. The goal is to capture a node's propagation influence from  
Figure 9: Analysis of user influence of a structural hole. multiple perspectives, resulting in a robust calculation of node influence across different levels. The propagation influence of user \(v\), denoted as \(Inf_{e}(v)\), is computed using the following formula:  
\[Inf_{e}(v)=\alpha PR(v)+\frac{1}{\beta C_{s}(v)}+\gamma C_{v} \tag{14}\]  
where \(PR(v)\) is the user's PageRank score, \(C_{s}(v)\) is the constraint coefficient representing the structural hole, and \(C_{v}\) is the clustering coefficient. The parameters \(\alpha\), \(\beta\), and \(\gamma\) are weights that sum to 1, meaning \(\alpha+\beta+\gamma=1\), and these values reflect the relative importance of each component.