  Isospectral transformations (IT) of matrices and networks allow for
compression of either object while keeping all the information about their
eigenvalues and eigenvectors.We analyze here what happens to generalized
eigenvectors under isospectral transformations and to what extent the initial
network can be reconstructed from its compressed image under IT. We also
generalize and essentially simplify the proof that eigenvectors are invariant
under isospectral transformations and generalize and clarify the notion of
spectral equivalence of networks.
