A material or object that allows charge to flow in one or more directions is said to be a conductor. Electrical conductors frequently use metals.
In graphite, every carbon is hybridized. Each carbon atom connects to three additional carbon atoms in the same plane to create a hexagonal array.
Because one of these bonds is a double-bond, the valency of carbon is satisfied.
The graphite structure is created by stacking the hexagonal arrays on top of one another.
A good conductor of electricity is graphite. This characteristic is mostly because of its structure. In graphite, covalent bonds hold only three carbon atoms together physically.
Since the fourth valence electron of a carbon atom is generally free and can move from one carbon atom to another, only three of its four valence electrons are utilized for bonding.
These free electrons are the reason why graphite is a good conductor of electricity.
Therefore, Yes graphite conducts electricity because its structure possesses free electrons.