# Hybrid Trust Model for Node-Centric Misbehavior Detection in Dynamic Behavior-Homogeneous Clusters
## 5 Mining of Complex Relationship Weights in Dynamic Vehicle Clusters
### Association Relationship Mining Based on Hypergraph Model  
A single vehicle node may belong to multiple clusters in dynamic vehicle clusters. To improve the accuracy of mixed trust values and reduce the influence of different association relationships on trust value calculation, it is necessary to further mine the authority of the node itself, the relationship between the node and vehicle clusters, and between  
Figure 4: Schematic diagram of dynamic vehicle clusters based on the hypergraph model.  
vehicle clusters. These relationships are then incorporated as influence weights to calculate subsequent mixed trust values.
* **Calculation of Vehicle Node Authority** Assuming that is the set of nodes \(S(v_{i})\) connected to vehicle node \(v_{i}\), and \(L(v_{i})\) is the number of directed edges connected to the node \(v_{i}\). The authority of \(v_{i}\) is represented as \(Au(v_{i})\), which is calculated as: \[Au(v_{i})=\frac{(1-d)}{N}+d\sum_{v_{i}\in S(v_{i})}\frac{Au(v_{j})}{E(v_{j})}\] (3)  
The authority of a node can be calculated using Equation (3), where the constant \(d,0<d<1\) is a damping factor typically set to 0.85 [25].
* **Mining of Association Relationships Between Vehicle Nodes** The model defines the association relationship between two vehicle nodes \(v_{i}\) and \(v_{j}\) as, in which \(\left|\right.\left|\right.\left|\right.\) represents the total number of hyperedges in the hypergraph: \[Re_{ij}(v_{i},v_{j})=\sum_{k=1}^{\left|\right.}\frac{h(v_{i},e_{k})\cdot h(v_ {j},e_{k})\cdot\omega_{e}}{\delta(e_{k})}\] (4) The more hyperedges two nodes share, the higher their degree of association.
* **Mining of Association Relationships Between Vehicle Nodes and Vehicle Clusters** Assume a vehicle node \(v_{i}\in V\), where \(V\) is a vehicle cluster. If hyperedge \(e_{i-j}\) and \(v_{i}\) the set of vehicle nodes in the same hyperedge as are given, then the association relationship between node \(v_{i}\) and vehicle cluster \(V\) is defined as: \[Rv_{i}(V)=\frac{\left|e_{i-j}\cap V\right|}{\left|V\right|}\] (5)  
The more vehicle nodes \(v_{i}\) in hyperedge \(e_{i-j}\) overlap with vehicle cluster \(V\), the higher the degree of association between node \(v_{i}\) and vehicle cluster \(V\), thus increasing the influence weight.
* **Mining of Association Relationships Between Vehicle Clusters** Assume two vehicle clusters \(C_{i}\) and \(C_{j}\). If there is a hyperedge between \(C_{i}\) and \(C_{j}\), then \(C_{i}\) and \(C_{j}\) are adjacent vehicle clusters. The association relationship between vehicle cluster \(C_{i}\) and \(C_{j}\) is defined as: \[R_{C}(i,j,t)=\max\{s(v_{i},v_{j},t)\big{|}v_{i}\in C_{i}\wedge v_{j}\in C_{j} \wedge\big{\{}v_{i},v_{j}\big{\}}\in E_{ij}\}\] (6) Here, \(E_{ij}\) represents a set of hyperedges in the hypergraph \(HG=(V,E,\omega)\) at time \(t\).  
This translation and summary explain how the hypergraph model is used to analyze the complex relationships within dynamic vehicle clusters, focusing on the authority of individual nodes, inter-node associations, and the relationships between nodes and clusters, as well as between different clusters. Using hypergraphs allows for a more nuanced understanding of these relationships, which is crucial for trust value calculations and anomaly detection in vehicular networks.