  The proximity-induced couplings in graphene due to the vicinity of a
ferromagnetic insulator are analyzed. We combine general symmetry principles
and simple tight-binding descriptions to consider different orientations of the
magnetization. We find that, in addition to a simple exchange field, a number
of other terms arise. Some of these terms act as magnetic orbital couplings,
and others are proximity-induced spin-orbit interactions. The couplings are of
similar order of magnitude, and depend on the orientation of the magnetization.
A variety of phases, and anomalous Hall effect regimes, are possible.
