  Error-tolerant graph matching gathers an important family of problems. These
problems aim at finding correspondences between two graphs while integrating an
error model. In the Graph Edit Distance (GED) problem, the insertion/deletion
of edges/nodes from one graph to another is explicitly expressed by the error
model. At the opposite, the problem commonly referred to as "graph matching"
does not explicitly express such operations. For decades, these two problems
have split the research community in two separated parts. It resulted in the
design of different solvers for the two problems. In this paper, we propose a
unification of both problems thanks to a single model. We give the proof that
the two problems are equivalent under a reformulation of the error models. This
unification makes possible the use on both problems of existing solving methods
from the two communities.
