Random networks: eigenvalue spectra

We analyze the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the spectra of networks with a local tree-like structure are presented. We propose a simple approximation, and in the framework of effective medium approximation, calculate spectra of various graphs analytically. We show that spectra of locally tree-like random graphs gives a good description of the spectral properties of real-life networks like the Internet.