  Hybrid graphene-superconductor devices have attracted much attention since
the early days of graphene research. So far, these studies have been limited to
the case of diffusive transport through graphene with poorly defined and modest
quality graphene-superconductor interfaces, usually combined with small
critical magnetic fields of the superconducting electrodes. Here we report
graphene based Josephson junctions with one-dimensional edge contacts of
Molybdenum Rhenium. The contacts exhibit a well defined, transparent interface
to the graphene, have a critical magnetic field of 8 Tesla at 4 Kelvin and the
graphene has a high quality due to its encapsulation in hexagonal boron
nitride. This allows us to study and exploit graphene Josephson junctions in a
new regime, characterized by ballistic transport. We find that the critical
current oscillates with the carrier density due to phase coherent interference
of the electrons and holes that carry the supercurrent caused by the formation
of a Fabry-P\'{e}rot cavity. Furthermore, relatively large supercurrents are
observed over unprecedented long distances of up to 1.5 $\mu$m. Finally, in the
quantum Hall regime we observe broken symmetry states while the contacts remain
superconducting. These achievements open up new avenues to exploit the Dirac
nature of graphene in interaction with the superconducting state.
