each carbon atom forms three covalent bonds with other carbon atoms
the carbon atoms form layers of hexagonal rings
there are no covalent bonds between the layers (weak bonds)
there is one non-bonded - or delocalised - electron from each atom
Properties and uses
Graphite has delocalised electrons, just like metals. These electrons are free to move between the layers in graphite, so graphite can conductelectricity. This makes graphite useful for electrodes in batteries and for electrolysis.
The forces between the layers in graphite are weak. This means that the layers can slide over each other. This makes graphite slippery, so it is useful as a lubricant.