  Vacancies in graphene have been proposed to give rise to $\pi$-like magnetism
in carbon materials, a conjecture which has been supported by recent
experimental evidence. A key element in this "vacancy magnetism" is the
formation of magnetic moments in vacancy-induced electronic states. In this
work we compute the charging energy $U$ of a single-vacancy generated localized
state for bulk graphene and graphene ribbons. We use a tight-binding model to
calculate the dependency of the charging energy $U$ on the amplitudes of the
localized wave function on the graphene lattice sites. We show that for bulk
graphene $U$ scales with the system size $L$ as $(\ln L)^{-2}$, confirming the
predictions in the literature, based on heuristic arguments. In contrast, we
find that for realistic system sizes $U$ is of the order of eV, a value that is
orders of magnitude higher than the previously reported estimates. Finally,
when edges are considered, we show that $U$ is very sensitive to the vacancy
position with respect to the graphene flake boundaries. In the case of armchair
nanoribbons, we find a strong enhancement of $U$ in certain vacancy positions
as compared to the value for vacancies in bulk graphene.
