Difference between the electrical conductivity of diamond and graphite are discussed as follows:
In graphite, each carbon atom is covalently bonded to only three neighboring carbon atoms and these form layers of hexagonal network which are separated by a large distance. The fourth valence electrons remain free which enable an easy flow of electron through graphite and that is why it is made a good conductor of electricity. But this does not happen in case of diamond. In diamond, each carbon atom makes bonds with four other carbon atoms. So there is no free electron with carbon atoms to conduct electricity.