The spin-dependent conductance and magnetoresistance (MR) in fcc Ni/graphene/fcc Ni (111) junctions are theoretically investigated. Assuming the Fermi energy at the Dirac points, we focus on conditions at the contact between the graphene and the fcc Ni layer to realize high MR ratios. Our findings are as following: band mixing between graphene and Ni should be rather weak, the effect of dopants on the MR is small for Ni electrodes, and a contact region of a few nanometers in size is sufficient to obtain high MR ratios. We further show that Ni-Co and Ni-Cu alloys are useful for electrode materials. The effect of roughness is also discussed. The increase in MR has been attributed to matching/mismatching of the Dirac point with the band structure of fcc Ni at the contact. The importance of the d orbitals of fcc Ni is also emphasized.