Dynamics of competitive information propagation on hypergraphs

To describe the significant group interactions and higher-order effects in competitive information spreading on real online social systems, this study constructs a competitive information spreading framework based on a single-layer hypergraph to characterize the competitive diffusion process of multiple types of information in group environments. In this model, both pairwise contact-based spreading and higher-order spreading driven by the overall opinion atmosphere within hyperedges are considered. Based on the proposed spreading mechanism, this paper develops the corresponding microscopic Markov chain dynamical equations and theoretically analyzes the outbreak threshold conditions under both single-information spreading and competitive spreading. Numerical simulations verify the validity of the analytical results and reveal various influences exerted by several key factors on competitive spreading behavior. The results show that a message type with a higher transmission rate is more likely to dominate in this competition, and higher-order interactions can further amplify that spreading ability for the dominant message type and accelerate its diffusion process. Compared with Poisson hypergraphs, the dominant information in power-law hypergraphs usually reaches a higher steady-state density. The steady-state survival regions of the two competing information types are mainly determined by their relative spreading abilities, and the analytically derived thresholds are highly consistent with the numerical results. In addition, the structural positions of initial spreader nodes can significantly affect the competition outcome, and may even enable information with a lower transmission rate to reverse the competition and finally survive. The intervention by fixed-state spreader nodes can also significantly enhance the competitive advantage of the corresponding information and effectively change the competition pattern. The present work offers a new analytical reference to understanding these spreading laws as well as regulation mechanisms of competitive information in higher-order group environments.