Extended model for carbon

The model of bonding involving unpaired electrons at an atom in its ground state must be extended when considering elemental forms of carbon. 
 
Diamond and graphite have significantly different properties to the elemental forms of the other nonmetals, as both are high-melting solids.  This suggests that they exist as structures in which large numbers of carbon atoms are bonded to one another.
 
How many bonds between carbons are suggested by the valence electron diagram?
The two unpaired electrons in this diagram suggest that carbon forms two bonds.
 
How many bonds does carbon form?
In its compounds carbon is involved in four bonds to other atoms (CH4 for example).

Thus all valence electrons on carbon can be shared with other atoms in bonds. 
 
 Group
Group
Group
Group 
 
 
   
   

With four unpaired electrons, a variety of bonding options are observed for carbon.  These can be shared with other atoms in 
four single bonds () as in CH4

two single bonds and a double bond () having two electrons shared with an adjacent atom.

one single bond and a triple bond () having three electrons are shared with an adjacent atom.

two double bonds () where two electrons are shared with two adjacent atoms

The first two of these are shown by considering the structures of graphite and diamond.