# Study of Information Dissemination in Hypernetworks with Adjustable Clustering Coefficient
## 1 Introduction  
The dissemination of information has greatly contributed to the advancement of human society. As science and technology continue to evolve, the integration of the Internet into people's daily life leads to an increasing frequency of information exchange. In social networks [1; 2; 3; 4], users' interdependence and cooperation serve as the basis for facilitating information dissemination. Therefore, identifying the mechanisms and characteristics of information diffusion is essential for both theoretical and practical purposes. Information dissemination refers to the process of spreading information from a source node to other nodes within a network, similar to how infectious diseases spread in populations. Research on propagation has focused on the study of network models and the study of propagation mechanisms. Network models include dynamic networks [5; 6; 7], scale-free networks [8; 9], node-weighted networks [10], edge-weighted networks [11], variable-growth networks [12], and correlation networks [13]. The study of propagation mechanisms includes SIS [14], SIR [15], etc. In cooperative complex networks, nodes represent individuals and edges represent cooperative relationships between individuals, such as scientific cooperative networks [16], corporate cooperative networks [17], and actor cooperative networks [18]. Previous studies have made significant contributions to the advancement of the field of spreading dynamics, and information propagation models based on complex networkshave been extensively explored. However, the complexity of real-life systems is often higher than what can be represented by the simple pairwise relations present in complex networks, calling for more intricate relationship descriptions. As a result, complex networks may not be able to fully capture the group characteristics in social networks. An alternative model for information propagation is the hypernetwork [19], which is constructed using the hypergraph theory. Unlike edges in conventional networks, hyperhedges in hypernetworks can accommodate a wide range of nodes and depict higher-order interactions among them. [PERSON] and [PERSON] [20] were the pioneers in the development of hypernetworks. They first introduced the concept and extended the notions of clustering coefficient and subgraph centrality to the hypernetwork model. Since then, several extensions to the model have been proposed, including directed hypernetworks by [PERSON] [21], hyperstructures by [PERSON] [22], and node importance metrics by [PERSON] [23]. Furthermore, the topological characteristics of hypernetworks have been thoroughly investigated by [PERSON] and [PERSON] [24]. In terms of dynamic evolution models, [PERSON] [25] proposed a nonuniform evolving hypergraph model with a nonlinear preferential attachment and an attractiveness. [PERSON] [26] proposed a hypernetwork evolution model that generated new hyperedges through the combination of an old node and several new nodes, while [PERSON] [27] presented a dynamic hypernetwork model that relied on growth and preferential attachment mechanisms. [PERSON] [28] later unified these models to propose a novel hypernetwork evolutionary model where old and new nodes generate multiple new hyperedges. Lastly, [PERSON] [12] proposed variable-growth hypernetworks, which saw the hyperedges and nodes undergo a growth over time. The application of hypernetworks has led to significant progress in the field of information propagation. However, the earlier works on hypernetwork models reviewed above commonly extend the mechanisms of complex networks for evolution. In actual social networks, clustering usually occurs. Friends of friends are more likely to form friendships, and academics or research teams in the same field are more likely to collaborate, which is not adequately captured by existing hypernetwork models. Thus, [PERSON] [29] proposed a hypernetwork model based on the aggregation phenomenon.