  We investigate the correspondence between the tight-binding Floquet
Hamiltonian of a periodically modulated honeycomb lattice and the Haldane
model. We show that - though the two systems share the same topological phase
diagram, as reported in a breakthrough experiment with ultracold atoms in a
stretched honeycomb lattice [Jotzu et al., Nature 515, 237 (2014)] - the
corresponding Hamiltonians are not equivalent, the one of the shaken lattice
presenting a much richer structure.
