To obtain an effective many-body model of graphene and related materials from first principles we calculate the partially screened frequency dependent Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction is U-00 = 9.3 eV in close vicinity to the critical value separating conducting graphene from an insulating phase emphasizing the importance of nonlocal Coulomb terms. The nearest-neighbor Coulomb interaction strength is computed to U-01 = 5.5 eV. In the long-wavelength limit, we find the effective background dielectric constant of graphite to be is an element of = 2.5 in very good agreement with experiment.