Fig. 7: Spectral signatures of network symmetry.
Laplacian spectrum of six test networks (blue) and of their quotient (red), given as relative probability of eigenvalue count, with multiplicity, in bins of size 0.1. Only the most significant part of the spectrum is shown. Most of the “peaks” observed in the spectral density occur at positive integers, as predicted. (Insets) Percentage of the high-multiplicity spectrum explained by the symmetry, as the ratio of \({\sum }_{{m}_{\lambda } \,{> }\,1}{m}_{\lambda }\) for the quotient eigenvalues, and for the Laplacian eigenvalues, where mλ is the multiplicity of an eigenvalue λ rounded to 8 decimal places.
