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The zigzag edges of graphene on Ir(111) are studied by ab initio simulations and low-temperature scanning tunneling spectroscopy, providing information about their structural, electronic, and magnetic properties. No edge state is found to exist, which is explained in terms of the interplay between a strong geometrical relaxation at the edge and a hybridization of the d orbitals of Ir atoms with the graphene orbitals at the edge.