  We employ the exact eigenstate basis formalism to study electrical
conductivity in graphene, in the presence of short-range diagonal disorder and
inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the
density of states is flat. We, then, make connection, using the MRG approach,
with the work of Abrahams \textit{et al.} and find a very good agreement for
disorder strength, $W$ = 5. For low disorder strength, $W$ = 2, we plot the
energy-resolved current matrix elements squared for different locations of the
Fermi energy from the band centre. We find that the states close to the band
centre are more extended and falls of nearly as $1/E_l^{2}$ as we move away
from the band centre. Further studies of current matrix elements versus
disorder strength suggests a cross-over from weakly localized to a very weakly
localized system. We calculate conductivity using Kubo Greenwood formula and
show that, for low disorder strength, conductivity is in a good qualitative
agreement with the experiments, even for the on-site disorder. The intensity
plots of the eigenstates also reveal clear signatures of puddle formation for
very small carrier concentration. We also make comparison with square lattice
and find that graphene is more easily localized when subject to disorder.
