  We propose a general approach to the description of spectra of complex
networks. For the spectra of networks with uncorrelated vertices (and a local
tree-like structure), exact equations are derived. These equations are
generalized to the case of networks with correlations between neighboring
vertices. The tail of the density of eigenvalues $\rho(\lambda)$ at large
$|\lambda|$ is related to the behavior of the vertex degree distribution $P(k)$
at large $k$. In particular, as $P(k) \sim k^{-\gamma}$, $\rho(\lambda) \sim
|\lambda|^{1-2\gamma}$. We propose a simple approximation, which enables us to
calculate spectra of various graphs analytically. We analyse spectra of various
complex networks and discuss the role of vertices of low degree. We show that
spectra of locally tree-like random graphs may serve as a starting point in the
analysis of spectral properties of real-world networks, e.g., of the Internet.
