Landau level quantization in graphene reflects the Dirac nature of its quasiparticles and has been found to exhibit an unusual integer quantum Hall effect. In particular the lowest Landau level can be thought as shared equally by electrons and holes and this leads to characteristic behaviour of the magneto-optical conductivity as a function of frequency $\Omega$ for various values of the chemical potential $\mu$. Particular attention is paid to the optical spectral weight under various absorption peaks and its redistribution as $\mu$ is varied. We also provide results for magnetic field $B$ as well as chemical potential sweeps at selected fixed frequencies which can be particularly useful for possible measurements in graphene. Both diagonal and Hall conductivity are considered.