  We derive the spectral properties of adjacency matrix of complex networks and
of their Laplacian by the replica method combined with a dynamical population
algorithm. By assuming the order parameter to be a product of Gaussian
distributions, the present theory provides a solution for the non linear
integral equations for the spectra density in random matrix theory of the
spectra of sparse random matrices making a step forward with respect to the
effective medium approximation (EMA) . We extend these results also to weighted
networks with weight-degree correlations
