title: Spectra of sparse regular graphs with loops.
abstract: We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary lengths. The implications of our results for the structural and dynamical properties of network models are discussed by showing how loops influence the size of the spectral gap and the propensity for synchronization. Analytical formulas for the spectrum are obtained for specific lengths of the loops.
authors.affiliation: Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Leuven, Belgium.
authors.forename: F L
authors.initials: FL
authors.lastname: Metz
authors.forename: I
authors.initials: I
authors.lastname: Neri
authors.forename: D
authors.initials: D
authors.lastname: Bollé
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003195:Computer Communication Networks; D015233:Models, Statistical; D010825:Physics / Q000379:methods; D015203:Reproducibility of Results; D012815:Signal Processing, Computer-Assisted; D013598:Systems Theory