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Randić et al. proposed a famous spectral graphical representation of DNA sequences, and claimed that it avoids loss of information. In this paper we build two mathematical models for this graphical representation and prove that the claim is correct, and that it also avoids degeneracy. Moreover, we propose a new method to do similarity analysis of DNA sequences based on the spectral representation. The method adopts M value to characterize a graphical representation and uses 24-component vector as descriptor. The approach is illustrated on the complete coding sequence of beta-globin genes from 7 different species.