  We have developed a variant transfer matrix method that is suitable for
transport through multi-probe systems. Using this method, we have numerically
studied the quantum spin Hall effect (QSHE) on 2D graphene with both intrinsic
(Vso) and Rashba (Vr) spin-orbit (SO) couplings. The integer QSHE arises in the
presence of intrinsic SO interaction and is gradually destroyed by the Rashba
SO interaction and disorder fluctuation. We have numerically determined the
phase boundaries separating integer QSHE and spin Hall liquid. We have found
that when Vso> 0.2t with t the hopping constant the energy gap needed for the
integer QSHE is the largest satisfying |E|<t. For smaller Vso the energy gap
decreases linearly. In the presence of Rashba SO interaction or disorders, the
energy gap diminishes. With Rashba SO interaction the integer QSHE is robust at
the largest energy within the energy gap while at the smallest energy within
the energy gap the integer QSHE is insensitive to the disorder.
