Atomic and electronic structure of simple metal/graphene and complex metal/graphene/metal interfaces Structural, electronic, and magnetic properties of simple interfaces (graphene on top of metallic substrate) and complex interfaces (a single metallic adlayer on a simple graphene/metal system, either on top or between the graphene and metallic substrate) have been studied using density functional theory. Two types of simple interfaces with strong (Ni/graphene) and weak (Cu/graphene) bonding were considered. In addition to binding energies and interface distances, which are used to quantify the strength of graphene-substrate interactions, the bonding in simple and complex interfaces was analyzed using charge density distributions and bond orders. Substantial enhancement of metallic substrate/graphene binding was observed in complex interfaces, consisting of Ni monolayer on top of simple {Ni or Cu}/graphene interface. The increase of substate-graphene bonding in such complex interfaces is accompanied by weakening in-plane C-C bonds in graphene, as quantified by the bond orders. A weak ferrimagnetism in graphene, i.e. unequal magnetic moments -0.04 µ B and +0.06 µ B on C atoms, is induced by a ferromagnetic Ni substrate. The strength of graphene-substrate interactions is also reflected in simulated STM images.