  The spatial dependence of the van der Waals (vdW) energy between graphene and
hexagonal boron-nitride (h-BN) is investigated using atomistic simulations. The
van der Waals energy between graphene and h-BN shows a hexagonal superlattice
structure identical to the observed Moir\'e pattern in the local density of
states (LDOS) which depends on the lattice mismatch and misorientation angle
between graphene and h-BN. Our results provide atomistic features of the weak
van der Waals interaction between graphene and BN which are in agreement with
experiment and provide an analytical expression for the size of the spatial
variation of the weak van der Waals interaction. We also found that the
A-B-lattice symmetry of graphene is broken a long the armchair direction.
