  Hall conductance $\sigma_{xy}$ as the Chern numbers of the Berry connection
in the magnetic Brillouin zone is calculated for a realistic multi band
tight-band model of graphene with non-orthogonal basis. It is confirmed that
the envelope of $\sigma_{xy}$ coincides with a semi-classical result when
magnetic field is sufficiently small.
  The Hall resistivity $\rho_{xy}$ from the weak-field Boltzmann theory also
explains the overall behaviour of the $\sigma_{xy}$ if the Fermi surface is
composed of a single energy band. The plateaux of $\sigma_{xy}$ are explained
from semi-classical quantization and necessary modification is proposed for the
Dirac fermion regimes.
