  We study complex networks under random matrix theory (RMT) framework. Using
nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the
eigenvalues of adjacency matrix of various model networks, namely, random,
scale-free and small-world networks. These distributions follow Gaussian
orthogonal ensemble statistic of RMT. To probe long-range correlations in the
eigenvalues we study spectral rigidity via $\Delta_3$ statistic of RMT as well.
It follows RMT prediction of linear behavior in semi-logarithmic scale with
slope being $\sim 1/\pi^2$. Random and scale-free networks follow RMT
prediction for very large scale. Small-world network follows it for
sufficiently large scale, but much less than the random and scale-free
networks.
