Since the discovery of graphene, this material is in the focus of intensive research in the field of electrochemical energy storage devices. Numerous experimental works demonstrate, however, contradictory results on the electron transfer kinetics at a graphene electrode, in particular, on electrocatalytic properties of graphene edges. In this work, we explore the spatially resolved electrochemistry of the basal plane and edge sites in the outer-sphere electron transfer step at the oxygen reduction reaction in acetonitrile solutions using theories and computations. We employ a quantum mechanical theory and explore the graphene-O2 orbital overlap resting on the results of density functional theory calculations and some data obtained earlier from molecular dynamics simulations. The zigzag graphene edges provide ca. 4 times faster electron transfer (in comparison with the basal plane) at long separations, >4 Å, i.e., in the diabatic regime. At the same time, effective rate constants obtained by integrating over the reaction layer do not reveal any noticeable difference for the basal plane and edge sites. It is argued that some experimental data can be explained only assuming a barrier layer separating the graphene surface and the O2 molecule.