Graphene epitaxially grown on Ru (0001) displays a remarkably ordered pattern of hills and valleys in scanning tunneling microscopy (STM) images. The extent to which the observed'ripples' are structural or electronic in origin has been much disputed recently. A combination of ultrahigh-resolution STM images and helium atom diffraction data shows that (i) the graphene lattice is rotated with respect to the lattice of Ru and (ii) the structural corrugation as determined from He diffraction is substantially smaller (0.15 Å) than predicted (1.5 Å) or reported from x-ray diffraction or low-energy electron diffraction. The electronic corrugation, on the contrary, is strong enough to invert the contrast between hills and valleys above+ 2.6 V as new, spatially localized electronic states enter the energy window of the STM. The large electronic corrugation results in a nanostructured periodic landscape of electron and hole pockets.