The carbon atom contains four electrons in its outermost shell that it can share to produce a stable electronic configuration, giving it a valency of four, indicating that it is tetravalent.
When one looks at the structural arrangement of graphite, one carbon atom is covalently bound to three other carbon atoms.
Because the fourth electron of each carbon atom is unbound, graphite conducts electricity.
As a result of the existence of free electrons in the structure, we may deduce that graphite is an excellent conductor of electricity.