  We present a topological description of quantum spin Hall effect (QSHE) in a
two-dimensional electron system on honeycomb lattice with both intrinsic and
Rashba spin-orbit couplings. We show that the topology of the band insulator
can be characterized by a $2\times 2$ traceless matrix of first Chern integers.
The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements
of the Chern number matrix (CNM). A spin Chern number is derived from the CNM,
which is conserved in the presence of finite disorder scattering and spin
nonconserving Rashba coupling. By using the Laughlin's gedanken experiment, we
numerically calculate the spin polarization and spin transfer rate of the
conducting edge states, and determine a phase diagram for the QSHE.
