We derive a message-passing method for computing the spectra of locally treelike networks
and an approximation to it that allows us to compute closed-form expressions or fast …

We propose a general approach to the description of spectra of complex networks. For the
spectra of networks with uncorrelated vertices (and a local treelike structure), exact …

Using methods from random matrix theory researchers have recently calculated the full
spectra of random networks with arbitrary degrees and with community structure. Both reveal …

We study random graphs with arbitrary distributions of expected degree and derive
expressions for the spectra of their adjacency and modularity matrices. We give a complete …

We analyze ensembles of random networks with fixed numbers of edges, triangles, and
nodes. In the limit as the number of nodes goes to infinity, this model is known to exhibit …

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 …

The asymptotic behavior of dynamical processes in networks can be expressed as a
function of spectral properties of the corresponding adjacency and Laplacian matrices …

We derive exact equations for the spectral density of sparse networks with an arbitrary
distribution of the number of single edges and triangles per node. These equations enable a …

Although the spectra of random networks have been studied for a long time, the influence of
network topology on the dense limit of network spectra remains poorly understood. By …

We present a simple yet rigorous approach to the determination of the spectral dimension of
random trees, based on the study of the massless limit of the Gaussian model on such trees …