  We introduce a number of random matrix models describing the Google matrix G
of directed networks. The properties of their spectra and eigenstates are
analyzed by numerical matrix diagonalization. We show that for certain models
it is possible to have an algebraic decay of PageRank vector with the exponent
similar to real directed networks. At the same time the spectrum has no
spectral gap and a broad distribution of eigenvalues in the complex plain. The
eigenstates of G are characterized by the Anderson transition from localized to
delocalized states and a mobility edge curve in the complex plane of
eigenvalues.
