Fundamental understanding of water confined in graphene is crucial to optimally design and operate sustainable energy, water desalination, and bio-medical systems. However, the current understanding predominantly remains in the static properties near the graphene surfaces. In this paper, a key water transport property, i. e., self-diffusivity, is examined under confinement by various graphene nanogap sizes (L-z = 0.7-4.17nm), using molecular dynamics simulations with various graphene-water interatomic potentials (Simple Point Charge (SPC/E) and TIP3P water models). It is found that the water self-diffusivity nearly linearly decreases as the graphene-water interatomic potential energy increases at a given nanogap size. It also decreases as the graphene nanogap size decreases down to L-z = 1.34 nm; however, it shows the peak water self-diffusivity at L-z = 0.8 nm and then continues to decrease. The peak water self-diffusivity is related to the significant change of the overlapping surface force, and associated, nonlinear local water density distribution. The in-plane water self-diffusivity is higher up to nearly an order of magnitude than that of the out-of-plane due to the geometrical confinement effect by the graphene nanogap. The obtained results provide a roadmap to fundamentally understand the water transport properties in the graphene geometries and surface interactions