  We analyze the nature of the single particle states, away from the Dirac
point, in the presence of long-range charge impurities in a tight-binding model
for electrons on a two-dimensional honeycomb lattice which is of direct
relevance for graphene. For a disorder potential
$V(\vec{r})=V_0\exp(-|\vec{r}-\vec{r}_{imp}|^2/\xi^2)$, we demonstrate that not
only the Dirac state but all the single particle states remain extended for
weak enough disorder. Based on our numerical calculations of inverse
participation ratio, dc conductivity, diffusion coefficient and the
localization length from time evolution dynamics of the wave packet, we show
that the threshold $V_{th}$ required to localize a single particle state of
energy $E(\vec{k})$ is minimum for the states near the band edge and is maximum
for states near the band center, implying a mobility edge starting from the
band edge for weak disorder and moving towards the band center as the disorder
strength increases. This can be explained in terms of the low energy
Hamiltonian at any point $\vec{k}$ which has the same nature as that at the
Dirac point. From the nature of the eigenfunctions it follows that a weak long
range impurity will cause weak anti localization effects, which can be
suppressed, giving localization if the strength of impurities is sufficiently
large to cause inter-valley scattering. The inter valley spacing $2|\vec{k}|$
increases as one moves in from the band edge towards the band center, which is
reflected in the behavior of $V_{th}$ and the mobility edge.
