  While usual edge states in the quantum Hall effect(QHE) reside between
adjacent Landau levels, QHE in graphene has a peculiar edge mode at E=0 that
reside right within the n=0 Landau level as protected by the chiral symmetry.
We have theoretically studied the edge states to show that the E=0 edge mode,
despite being embedded in the bulk Landau level, does give rise to a wave
function whose charge is accumulated along zigzag edges. This property, totally
outside continuum models, implies that the graphene QHE harbors edges distinct
from ordinary QHE edges with their topological origin. In the charge
accumulation the bulk states re-distribute their charge significantly, which
may be called a topological compensation of charge density. The real space
behavior obtained here should be observable in an STM imaging.
