  Electrical transport in graphene offers a fascinating parallel to spin
transport in semiconductors including the spin-Hall effect. In the weak
momentum scattering regime the steady-state density matrix contains two
contributions, one linear in the carrier number density $n$ and characteristic
scattering time $\tau$, the other independent of either. In this paper we take
the Liouville equation as our starting point and demonstrate that these two
contributions can be identified with pseudospin conservation and
non-conservation respectively, and are connected in a non-trivial manner by
scattering processes. The scattering term has a distinct form, which is
peculiar to graphene and has important consequences in transport. The
contribution linear in $\tau$ is analogous to the part of the spin density
matrix which yields a steady state spin density, while the contribution
independent of $\tau$, is analogous to the part of the spin density matrix
which yields a steady state spin current. Unlike in systems with spin-orbit
interactions, the $n$ and $\tau$-independent part of the conductivity is
reinforced in the weak momentum scattering regime by scattering between the
conserved and non-conserved pseudospin distributions.
