Spectral analysis – the study of the properties of the eigenvalues associated with some matrix derived from an underlying graph form – has proven to offer valuable insights in many domains where graph-theoretic models are prevalent. Abstract argumentation frameworks (afs) are, of course, one such model and have provided a unifying basis for defining semantic properties related to concepts of “argument acceptability”. In this paper we consider the possible benefits of adopting spectral methods as a tool for analysing argumentation structures, presenting a preliminary empirical study of semantics in afs and properties of the associated spectrum.