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Diamond is extremely unreactive, and in contrast graphite is quite reactive.
In diamond each C atom is tetrahedrally surrounded by four othr C atoms, each at a distance of 1.54A. The tetrahedra are linked together into a three-dimensional giant molecule. The unit cell is cubic. Strong covalent bonds extend in all directions. Thus the melting point is abnormally high (about 3930 deg C) and the structure is very hard.
Graphite is composed of flat 2-dimensional sheets of carbon atoms. Each sheet is a hexagonal net of C atoms, and may be regarded as a fused system of benzene rings. The layers are held together by relatively weak van der Waals forces. In graphite only three of the valency electrons of each carbon atom are involved in forming sigma bonds (using sp2 hybrid orbitals). The fourth electron forms a pi bond. The pi electrons are delocalized over the whole sheet, and as they are mobile, graphite conducts electricity. Conduction can occur in a sheet, but not from one sheet to another.
I hope this can help your understanding. =)