  We investigate realizations of topological insulators with spin-1 bosons
loaded in a honeycomb optical lattice and subjected to a $SU(3)$ spin-orbit
coupling - a situation which can be realized experimentally using cold atomic
gases. In this paper, we focus on the topological properties of the
single-particle band structure, namely Chern numbers (lattice with periodic
boundary conditions) and edge states (lattice with strip geometry). While
$SU(2)$ spin-orbit couplings always lead to time-reversal symmetric Hubbard
models, and thereby to topologically trivial band structures, suitable $SU(3)$
spin-orbit couplings can break time reversal symmetry and lead to topologically
non-trivial bulk band structures and to edge states in the strip geometry. In
addition, we show that one can trigger a series of topological transitions
(i.e. integer changes of the Chern numbers) that are specific to the geometry
of the honeycomb lattice by varying a single parameter in the Hamiltonian.
