  We define and discuss the utility of two equivalence graph classes over which
a spectral projector-based graph Fourier transform is equivalent: isomorphic
equivalence classes and Jordan equivalence classes. Isomorphic equivalence
classes show that the transform is equivalent up to a permutation on the node
labels. Jordan equivalence classes permit identical transforms over graphs of
nonidentical topologies and allow a basis-invariant characterization of total
variation orderings of the spectral components. Methods to exploit these
classes to reduce computation time of the transform as well as limitations are
discussed.
