The structural properties of graphene/Ni(111) are investigated by a combination of low-energy electron diffraction (LEED), x-ray photoelectron spectroscopy (XPS), angle-scanned photoelectron diffraction (PED), and first-principles calculations. XPS data indicate that graphene interacts strongly with the topmost Ni layer. Diffraction data show that graphene is deposited commensurably with the underlying Ni surface atoms. Twelve different graphene preparations were analyzed by LEED and one by PED. Considering the relative position between the carbon and Ni atoms, five experimental sets indicate a top-fcc structure, three show a bridge-top structure, and four have a mixed structure. The analysis of the PED experiment suggests the top-fcc termination. Our first-principles calculations show that the total energies of the top-fcc and bridge-top structures are nearly degenerate, which corroborates the observed bistability of those phases. Moreover, by comparing the structural parameters obtained by the three methods (LEED, PED, and ab initio calculations), excellent agreement is achieved.