2026/01/08 by Jaume Llabrés, Raúl Toral, Maxi San Miguel +1 · 1 voice
Decision Sciences · Physics and Astronomy · #Complex Network Analysis Techniques #Game Theory and Applications #Opinion Dynamics and Social Influence #physics.soc-ph
paper · pdf · doi:10.1103/wy1x-3px8
openalex publication_date 2026/05/09 · openalex created_date 2026/05/10 · openalex updated_date 2026/07/28
We show that a general class of node-update social impact models with higher-order interactions on hypergraphs can be exactly mapped to an equivalent model with pairwise interactions on a weighted projected network. This mapping preserves the microscopic probabilities of changing the state of the nodes. As a particular case, we introduce hypergraph-voter models, for which we compute the weights of the projected network, both analytically and numerically, across several hypergraph ensembles, and we characterize their ordering dynamics through simulations of both higher-order and reduced pairwise dynamics. For a linear social impact function (), the weights of the projected network are static (state-independent), allowing us to develop a pair approximation that describes with accuracy the time evolution of macroscopic observables, which turn out to be independent of those weights. The macroscopic dynamics is thus equivalent to that of the standard voter model on the unweighted projected network. For a power-law social impact function (), the weights of the projected network depend on the instantaneous system configuration. Nevertheless, the nonlinear voter model on the unweighted projected network still reproduces the main macroscopic trends for well-connected hypergraphs.