  An edge-operation on a graph $G$ is defined to be either the deletion of an
existing edge or the addition of a nonexisting edge. Given a family of graphs
$\mathcal{G}$, the editing distance from $G$ to $\mathcal{G}$ is the smallest
number of edge-operations needed to modify $G$ into a graph from $\mathcal{G}$.
In this paper, we fix a graph $H$ and consider ${\rm Forb}(n,H)$, the set of
all graphs on $n$ vertices that have no induced copy of $H$. We provide bounds
for the maximum over all $n$-vertex graphs $G$ of the editing distance from $G$
to ${\rm Forb}(n,H)$, using an invariant we call the {\it binary chromatic
number} of the graph $H$. We give asymptotically tight bounds for that distance
when $H$ is self-complementary and exact results for several small graphs $H$.
