Most of the carbon compounds do not conduct electricity because they have low melting and boiling points.Nature of bonding in carbon compounds is different from that observed in ionic compounds thus they are poor conductors of electricity.Bonding in carbon compounds does not involve the formation of ions which indicates the absence of ions in carbon compounds.So we can say that in carbon compounds, the bonding between carbon and other atoms is non-ionic in nature.
Carbon compounds do not conduct electricity . the compounds which form ionic bond or forms ions conduct electricity . but carbon does not form ionic bond it forms only covalent bonds share its electrons but does not form ions. other reasons are that it has low melting points and boiling points.the only allotrop of carbon that is graphite is a conductor .