  We apply random matrix theory to complex networks. We show that nearest
neighbor spacing distribution of the eigenvalues of the adjacency matrices of
various model networks, namely scale-free, small-world and random networks
follow universal Gaussian orthogonal ensemble statistics of random matrix
theory. Secondly we show an analogy between the onset of small-world behavior,
quantified by the structural properties of networks, and the transition from
Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody
parameter characterizing a spectral property. We also present our analysis for
a protein-protein interaction network in budding yeast.
