Growth of nanocrystalline graphene films on (6√3 × 6√3)R30°-reconstructed SiC surfaces was achieved by molecular beam epitaxy, enabling the investigation of quasi-homoepitaxial growth. The structural quality of the graphene films, which is investigated by Raman spectroscopy, increases with growth time. X-ray photoelectron spectroscopy proves that the SiC surface reconstruction persists throughout the growth process and that the synthesized films consist of sp2-bonded carbon. Interestingly, grazing incidence x-ray diffraction measurements show that the graphene domains possess one single in-plane orientation, are aligned to the substrate, and offer a noticeably contracted lattice parameter of 2.450 Å. We correlate this contraction with theoretically calculated reference values (all-electron density functional calculations based on the van der Waals corrected Perdew-Burke-Ernzerhof functional) for the lattice parameter contraction induced in ideal, free-standing graphene sheets by: substrate-induced buckling, the edges of limited-size flakes and typical point defects (monovacancies, divacancies, Stone-Wales defects). © IOP Publishing and Deutsche Physikalische Gesellschaft.