# Study of Information Dissemination in Hypernetworks with Adjustable Clustering Coefficient
## 4 Simulation Results and Analysis
### The Results of Information Communication Theory Analysis
#### 4.2.6 The Influence of Structural Parameters \(m_{1}\), \(m_{2}\), and \(m\)  
Effect of \(m_{1}\) In this paper, \(m_{1}\) denotes the number of new nodes that join the hypernetwork at each time step. In order to investigate how \(m_{1}\) influences the propagation process, the following parameters were established: \(m_{0}=4\), \(m_{1}=1,3,5\), \(m_{2}=3\), \(m=3\), \(\beta=0.1\), \(\gamma=0.1\), and \(p=0.6\). The information propagation curves for various \(m_{1}\) values are presented in Figure 11. As depicted in the figure, the curves exhibit slight differences, and the information propagation accelerates with increasing \(m_{1}\) values. It can be concluded that an increase in \(m_{1}\) can promote information dissemination, but the change is not very significant.  
3. Effect of \(m_{1}+m_{2}\)  
The number of neighboring nodes for a specific node is directly connected to both the dissemination process and outcomes of information, which are jointly determined by \(m_{1}\) and \(m_{2}\). Therefore, we set the parameters as \(m_{0}=6\), \(m_{1}=1,3,5\), \(m_{2}=1,3,5\), \(m=3\), \(\beta=0.1\), \(\gamma=0.1\), and \(p=0.6\) to explore the impact of \(m_{1}\) and \(m_{2}\). The information dissemination curves for different \(m_{1}+m_{2}\) values are presented in Figure 13a. As demonstrated, the larger the value of \(m_{1}+m_{2}\), the shorter the amount of time needed for the information to reach a stable state, and the larger the value of the steady-state phase. Additionally, we set identical values for \(m_{1}+m_{2}\) but different values for \(m_{1}\) and \(m_{2}\), as shown below: \(m_{1}=1,3,5\), \(m_{2}=5,3,1\). The information propagation curve is presented in Figure 13b. As seen in the figure, the density of I-state nodes is almost the same in the steady-state phase in the three cases. Importantly, for the same \(m_{1}+m_{2}\) value, higher \(m_{2}\) values result in a faster system to reach the steady state. This discovery implies that an increased number of  
Figure 11: Information propagation curves of different \(m_{1}\)’s.  
Figure 12: Information propagation curves of different \(m_{2}\)’s.  
neighboring nodes of I-state nodes accelerates the rate of information propagation. This observation aligns with the theoretical analysis presented in Section 3.2.  
4. Effect of \(m\)  
Here, \(m\) signifies the number of generated hyperedges generated every time a new node is added. To explore how \(m\) affects the propagation process, we set \(m_{0}=6\), \(m_{1}=3\), \(m_{2}=3\), \(\beta=0.1\), \(\gamma=0.1\), \(p=0.6\), and \(m=1,3,5\). The information propagation graph is presented in Figure 14. As the number of hyperedges generated per new node addition increases, nodes become more closely connected, and the entire network becomes more interconnected. Therefore, larger \(m\) values boost the information propagation efficiency, resulting in higher steady-state values.  
Figure 13: The evolution of information dissemination with different values of \(m_{1}+m_{2}\).