Eigenvalue spacings for regular graphs

Abstract

We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix theory as we increase the number of vertices. A review of the basic facts on graphs and their spectra is included.

Appeared in IMA vol. 109 (Emerging applications of number theory, Minneapolis, MN 1996)