  Even though graphene is a low energy system consisting of the two dimensional
honeycomb lattice of carbon atoms, its quasi-particle excitations are fully
described by the 2+1 dimensional relativistic Dirac equation. In this paper we
show that while the spin-orbit interaction in graphene is of the order of $4
meV$, it opens up a gap of the order of $10^{-3} meV$ at the Dirac points. We
present the first principle calculation of the spin-orbit gap, and explain the
behavior in terms of a simple tight-binding model. Our result also shows that
the recently predicted quantum spin Hall effect in graphene can only occur at
unrealistically low temperature.
