The mean-field approximation based on the Gibbs-Bogoliubov inequality and Monte Carlo simulations based on the Metropolis method in the Blume–Emery–Griffiths model were used to successfully examine a hexagonal Ising nanowire with spin-1. It was found that the model displays fascinating phase diagrams in various planes of interest by using both methods. The investigation of magnetic hysteresis cycles also exhibits interesting properties. The model not only presents first- and second-order phase transition lines, but also the tricritical and isolated critical points, multi-compensation temperatures, and magnetic hysteresis behavior with one to eight cycles. •The mean-field approximation based on the Gibbs-Bogoliubov inequality is applied.•The Monte Carlo simulations based on the Metropolis method is employed.•Spin-1 Blume–Emery–Griffiths model for hexagonal Ising nanowire is investigated.•First- and second-order transitions, tricritical and isolated critical points are found.•Multi-compensation and magnetic hysteresis with one to eight cycles are observed.