  We report a theoretical investigation of quantized spin-Hall conductance
fluctuation of graphene devices in the diffusive regime. Two graphene models
that exhibit quantized spin-Hall effect (QSHE) are analyzed. Model-I is with
unitary symmetry under an external magnetic field $B\ne 0$ but with zero
spin-orbit interaction, $t_{SO}=0$. Model-II is with symplectic symmetry where
B=0 but $t_{SO} \ne 0$. Extensive numerical calculations indicate that the two
models have exactly the same universal QSHE conductance fluctuation value
$0.285 e/4\pi$ regardless of the symmetry. Qualitatively different from the
conventional charge and spin universal conductance distributions, in the
presence of edge states the spin-Hall conductance shows an one-sided log-normal
distribution rather than a Gaussian distribution. Our results strongly suggest
that the quantized spin-Hall conductance fluctuation belongs to a new
universality class.
