Each carbon atom in diamond forms four single covalent bonds with surrounding carbon atoms. The total number of bonds would depend on the sample size.
Diamond exhibits covalent network bonding and forms what's called a giant covalent structure or a giant molecular structure. This is a crystal lattice-type structure in which each atom is joined to adjacent atoms by covalent bonds, not by electrostatic attraction as seen in ionic crystal lattices.
Giant molecular solids are very hard and have very high melting points due to the many bonds present. Diamond is the hardest mineral. In comparison, graphite, which is another form of pure carbon, is very soft. It doesn't have covalent network bonding. It forms layers in which each atom is bonded to three adjacent atoms In the same plane. The layers of graphite aren't bonded together so they can slide past each other.
Quartz, which is silicon dioxide, is another example of a giant molecular solid. Like diamond, it's a crystal structure that's hard and has a high melting point.