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Isospectral transformations (IT) of matrices and networks allow forcompression of either object while keeping all the information about theireigenvalues and eigenvectors.We analyze here what happens to generalizedeigenvectors under isospectral transformations and to what extent the initialnetwork can be reconstructed from its compressed image under IT. We alsogeneralize and essentially simplify the proof that eigenvectors are invariantunder isospectral transformations and generalize and clarify the notion ofspectral equivalence of networks.

Generalized Eigenvectors of Isospectral Transformations,Spectral Equivalence and Reconstruction of Original Networks