  The moir\'e superlattice induced in graphene by the hexagonal boron nitride
substrate modifies strongly the bandstructure of graphene, which manifests
itself by the appearance of new Dirac points, accompanied by van Hove
singularities. In this work, we present supercurrent measurements in a
Josephson junction made from such a graphene superlattice in the long and
diffusive regime, where that the supercurrent depends on the Thouless energy.
We can then estimate the specific density of states of the graphene
superlattice from the combined measurement of the critical current and the
normal state resistance. The result matches with theoretical predictions and
highlights the strong increase of the density of states at the van Hove
singularities. By measuring the magnetic field dependence of the supercurrent,
we find the presence of edge currents at these singularities. We explain it by
the reduction of the Fermi velocity associated with the flat band at the van
Hove singularity, which suppresses the supercurrent in the bulk while the
electrons at the edge remain less localized, resulting in an edge supercurrent.
We attribute this different behavior of the edges to defects or chemical
doping.
