Opinion Dynamics on Higher-Order Social Networks: A Continuous-Time Perspective

Opinion dynamics models that elucidate the evolution and formation of opinions conventionally focus on pairwise interactions within graphs, often overlooking the complex higher-order interactions that arise in real-world social networks, such as online meetings and group chats. In this article, a continuous-time dynamical system is developed to study opinion-forming processes over higher-order networks associated with undirected hypergraphs. The proposed model introduces a novel diffusion-like interaction function to characterize interactions of different orders over hypergraphs. The convergence and stability of the dynamical systems are further examined in both the presence and absence of stubborn individuals. Building on traditional opinion dynamics models and integrating weak-tie theory, we emphasize the critical role of higher-order interactions in shaping individual opinions, enhancing network communication efficiency, and mitigating opinion polarization. Finally, all theoretical results are extensively investigated and empirically validated through numerical experiments on both synthetic and real-world network datasets.