  Recently unusual integer quantum Hall effect was observed in graphene in
which the Hall conductivity is quantized as $\sigma_{xy}=(\pm 2, \pm 6, \pm 10,
>...) \times \frac{e^2}{h}$, where $e$ is the electron charge and $h$ is the
Planck constant. %\cite{Novoselov2005,Zheng2005}, %although it can be explained
in the argument of massless Dirac fermions, To explain this we consider the
energy structure as a function of magnetic field (the Hofstadter butterfly
diagram) on the honeycomb lattice and the Streda formula for Hall conductivity.
The quantized Hall conductivity is obtained to be odd integer, $\pm1, \pm3,
\pm5, ...$ times two (spin degrees of freedom) when a uniform magnetic field is
as high as 30T for example. When the system is anisotropic and described by the
generalized honeycomb lattice, Hall conductivity can be quantized to be any
integer number. We also compare the results with those for the square lattice
under extremely strong magnetic field.
