This paper describes a novel framework for comparing and matching corrupted relational graphs. The normalized edit distance of Marzal and Vidal can used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare this criterion with that recently reported by Wilson and Hancock.The use of edit distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data, and illustrate its effectiveness on an uncalibrated stereo correspondence problem.