Opinion dynamics is a central subject of computational social science, and various models have been developed to understand the evolution and formulation of opinions. Existing models mainly focus on opinion dynamics on graphs that only capture pairwise interactions between agents. In this paper, we extend the popular Friedkin-Johnsen model for opinion dynamics on graphs to hypergraphs, which describe higher-order interactions occurring frequently on real networks, especially social networks. To achieve this, based on the fact that for linear dynamics the multi-way interactions can be reduced to effective pairwise node interactions, we propose a method to decode the group interactions encoded in hyperedges by undirected edges or directed edges in graphs. We then show that higher-order interactions play an important role in the opinion dynamics, since the overall steady-state expressed opinion and polarization differ greatly from those without group interactions. We also provide an interpretation of the equilibrium expressed opinion from the perspective of the spanning converging forest, based on which we design a fast sampling algorithm to approximately evaluate the overall opinion and opinion polarization on directed weighted graphs. Finally, we conduct experiments on real-world hypergraph datasets, demonstrating the performance of our algorithm.

翻译：观点动力学是计算社会科学的核心课题，为理解观点的演化与形成，学界已发展出多种模型。现有模型主要关注图结构上的观点动力学，仅能捕捉个体间的成对交互。本文将该领域著名的弗里德金-约翰森模型从图结构推广至超图，后者能够描述现实网络（特别是社交网络）中频繁出现的高阶交互。为实现这一目标，基于线性动力学中多元交互可简化为有效成对节点交互这一事实，我们提出一种方法：通过图中的无向边或有向边解码超边编码的群体交互。研究表明，高阶交互在观点动力学中扮演重要角色——引入群体交互后，系统稳态的表达观点与极化程度与无群体交互情形存在显著差异。我们还从生成收敛森林的视角对平衡态表达观点提出新解释，并据此设计快速采样算法以近似评估有向加权图上的整体观点与观点极化。最后，在真实超图数据集上的实验验证了所提算法的性能。