  We show that the singular loci of graph hypersurfaces correspond
set-theoretically to their rank loci. The proof holds for all configuration
hypersurfaces and depends only on linear algebra. To make the conclusion for
the second graph hypersurface, we prove that the second graph polynomial is a
configuration polynomial. The result indicates that there may be a fruitful
interplay between the current research in graph hypersurfaces and Stratified
Morse Theory.
