In one embodiment, a composition of matter includes: a plurality of ligaments each independently comprising one or more layers of graphene; where the plurality of ligaments are arranged according to a deterministic three-dimensional (3D) pattern. In another embodiment, a method of forming a deterministic three-dimensional (3D) architecture of graphene includes: forming or providing a substrate structurally characterized by a predefined 3D pattern; forming one or more layers of metal on surfaces of the substrate; and forming one or more layers of graphene on surfaces of the metal.