Graphite is a non-metal which conducts electricity.
This crystal carbon has a structure that is planar and layered. Graphene is the term used to denote each layer of the same. The graphite would be conducive electrically owing to the fourth electron having a chance to migrate into the plane. The layers of the carbon crystal could swiftly move past each other as the layers could be separated easily as van der Waals bonds that are weak-hold them together.