  Statistical graph models aim at modeling graphs as random realization among a
set of possible graphs. One issue is to evaluate whether or not a graph is
likely to have been generated by one particular model. In this paper we
introduce the edit distance expected value (EDEV) and compare it with other
methods such as entropy and distance to the barycenter. We show that contrary
to them, EDEV is able to distinguish between graphs that have a typical
structure with respect to a model, and those that do not. Finally we introduce
a statistical hypothesis testing methodology based on this distance to evaluate
the relevance of a candidate model with respect to an observed graph.
