  The analytical expressions for both diagonal and off-diagonal ac and dc
conductivities of graphene placed in an external magnetic field are derived.
These conductivities exhibit rather unusual behavior as functions of frequency,
chemical potential and applied field which is caused by the fact that the
quasiparticle excitations in graphene are Dirac-like. One of the most striking
effects observed in graphene is the odd integer quantum Hall effect. We argue
that it is caused by the anomalous properties of the Dirac quasiparticles from
the lowest Landau level. Other quantities such as Hall angle and Nernst signal
also exhibit rather unusual behavior, in particular when there is an excitonic
gap in the spectrum of the Dirac quasiparticle excitations.
