  A tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method
is used to describe disordered single-layer graphene Josephson junctions.
Scattering by vacancies, ripples or charged impurities is included. We compute
the Josephson current and investigate the nature of multiple Andreev
reflections, which induce bound states appearing as peaks in the density of
states for energies below the superconducting gap. In the presence of single
atom vacancies, we observe a strong suppression of the supercurrent that is a
consequence of strong inter-valley scattering. Although lattice deformations
should not induce inter-valley scattering, we find that the supercurrent is
still suppressed, which is due to the presence of pseudo-magnetic barriers. For
charged impurities, we consider two cases depending on whether the average
doping is zero, i.e. existence of electron-hole puddles, or finite. In both
cases, short range impurities strongly affect the supercurrent, similar to the
vacancies scenario.
