2026 Workshop Sistemas Complexos (Aracaju)
Higher-order q-voter model with majority thresholds
FASSONI, T.\(^{1}\)\(^{\star}\), COTA, W.\(^1\), FERREIRA, S.\(^1\)
¹ Departamento de Física, Universidade Federal de Viçosa, Viçosa – MG.
timoteo.fassoni@ufv.br
RESUMO
The central paradigm in the study of complex systems has been the description in pairwise networks. However, phenomena such as human communication have, by nature, interactions that can involve three or more agents simultaneously. To model these systems with group interactions, one must resort to higher-order networks (HON), a natural extension of the dyadic counterpart, allowing the mutual interaction of several vertices simultaneously – that is, belonging to the same hyperedge. In particular, there is a growing interest in studying opinion dynamics on HONs, as they are governed by group interactions, which can have several individuals. The voter model is one of the first proposed for the study of opinion dynamics; however, it simplifies the process by considering the influence of a single neighbor at a time, ignoring the simultaneous action of multiple individuals on an agent. A natural way to extend this idea to include complex contagion is to require that the state change depends on the influence of q neighbors, originating the q-voter model. This work generalizes the q-voter model to hypergraphs. Our formulation establishes that a hyperedge only influences a target agent if it reaches an internal state of consensus, defined by a tunable majority threshold; otherwise, it is considered fragmented and, effectively, inactive. Analytically, by deriving the microscopic transition rates, we developed a mean-field theory for the macroscopic magnetization that preserves key properties of the universality class, such as Z2 symmetry and absorbing states. Computationally, we implemented a continuous-time Gillespie algorithm for optimized simulations. Preliminary results on uniform Random Regular Networks (RRNs) reveal interesting higher-order effects, such as a non-monotonic dependence of the consensus time on the hyperedge order. We are currently expanding our simulations to complete and heterogeneous hypergraphs to further explore our analytical equations and phenomena. Acknowledgments: FAPEMIG, CAPES, CNPq.
Palavras-chave: higher-order networks, q-voter model, opinion dynamics.