Spectral properties of the Apollonian network

A first characterization of the spectral properties of the Apollonian network is presented. Results are based on the numerically evaluated eigenvalue spectra of adjacency matrices for the first nine generations of the network. The main features refer to the presence of several gaps on the eigenvalue axis and a very large number of degenerated eigenvalues. The increase in the degeneracy of a family of eigenvalues is found to obey a very simple empirical relation.