  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.
