  The experimental study of edge states in atomically-thin layered materials
remains a challenge due to the difficult control of the geometry of the sample
terminations, the stability of dangling bonds and the need to measure local
properties. In the case of graphene, localised edge modes have been predicted
in zig-zag and bearded edges, characterised by flat dispersions connecting the
Dirac points. Polaritons in semiconductor microcavities have recently emerged
as an extraordinary photonic platform to emulate 1D and 2D Hamiltonians,
allowing the direct visualization of the wavefunctions in both real- and
momentum-space as well as of the energy dispersion of eigenstates via
photoluminescence experiments. Here we report on the observation of edge states
in a honeycomb lattice of coupled micropillars. The lowest two bands of this
structure arise from the coupling of the lowest energy modes of the
micropillars, and emulate the {\pi} and {\pi}* bands of graphene. We show the
momentum space dispersion of the edge states associated to the zig-zag and
bearded edges, holding unidimensional quasi-flat bands. Additionally, we
evaluate polarisation effects characteristic of polaritons on the properties of
these states.
