  We analyze eigenvalues fluctuations of the Laplacian of various networks
under the random matrix theory framework. Analyses of random networks,
scale-free networks and small-world networks show that nearest neighbor spacing
distribution of the Laplacian of these networks follow Gaussian orthogonal
ensemble statistics of random matrix theory. Furthermore, we study nearest
neighbor spacing distribution as a function of the random connections and find
that transition to the Gaussian orthogonal ensemble statistics occurs at the
small-world transition.
