The electrons in each carbon atom are arranged in different orbitals. Two electrons occupy the inner spherical 1S shell. Then 2S and 2P accommodate the remaining four electrons. In a molecule, 2S and 2P are modified to create a hybridized SP2 bonding orbital. This has three equal lobes pointing outwards in a a plane and connecting to adjacent carbon atoms (translucent blue sausage like connecting bodies in this diagram). The fourth electron in this outer shell occupies a pi orbital (not shown) that projects above and below the molecular plane. See our graphene pi orbital graphic.This pi orbital merges with adjacent pi orbitals creating a huge orbital which allows easy movement of electrons across the plane of the molecule. This is what gives graphene its remarkable electrical conductivity.