  We investigate the properties of magnon edge states in a ferromagnetic
honeycomb spin lattice with a Dzyaloshinskii-Moriya interaction (DMI). We
derive analytical expressions for the energy spectra and wavefunctions of the
edge states localized on the boundaries. By introducing an external on-site
potential at the outermost sites, we show that the bosonic band structure is
similar to that of the fermionic graphene. We investigate the region in the
momentum space where the bosonic edge states are well defined and we analyze
the width of the edge state and their dependence with DMI strength. Our
findings extend the predictions using topological arguments and they allow
size-dependent confirmation from possible experiments
