Localization of atomic defect-induced electronic transport through a single graphene layer is calculated using a full-valence electronic structure description as a function of the defect density and taking into account the atomic-scale deformations of the layer. The elementary electronic destructive interferences leading to Anderson localization are analyzed. The low-voltage current intensity decreases with increasing length and defect density, with a calculated localization length ζ = 3.5 nm for a defect density of 5%. The difference from the experimental defect density of 0.5% required for an oxide surface-supported graphene to obtain the same ζ is discussed, pointing out how interactions of the graphene supporting surface and surface chemical modifications also control electronic transport localization.