For a Bayes classifier whose input space is a graph, we study the structure of the boundary, which comprises those points for which at least one neighbor is classified differently. The scientific setting is assignment of DNA reads produced by next generations sequencers to candidate source genomes. We show that the boundary is both large and complicated in structure. A new measure of uncertainty, Neighbor Similarity, which compares the classifier result for an input point to the distribution of results for its neighbors, not only tracks two inherent uncertainty measures for the Bayes classifier, but also can be implemented for classifiers without inherent measures of uncertainty.