The majority of realistic neworks (Internet, collaborations, cellular networks, etc.) show the scale-free property for the distribution of the node-connectivity [1,2]. The connectivity matrix can be associated with the network and the eigenproblem for this matrix can be formulated. It has been found that the distribution of the eigenvalues shows some universal features. The aim of the project is to derive this universal functional form within the frame of certain approximations (mean-field). We have already obtained the solution in the virtual-crystal approximation and the applicant is supposed to improve the quality of the approximations.

Once the spectral density of the scale-free network is found, then the results can be used in the study of the information propagation through the network. This part of the project is optional.