In the study of the spectra of power-law graphs, there are basically two competing
approaches. One is to prove analogues of Wigner's semicircle law, whereas the other …

Many graphs arising in various information networks exhibit the" power law" behavior–the
number of vertices of degree k is proportional to k-β for some positive β. We show that if β> …

We consider random graphs such that each edge is determined by an independent random
variable, where the probability of each edge is not assumed to be equal. We use a Chernoff …

Let G=(V, E) be a graph with vertex set V (G)={1,..., n}. The adjacency matrix of G, denoted by
A= A (G), is the n-by-n 0, 1-matrix whose entry Aij is one if (i, j)∈ E (G), and is zero …

We study numerically and analytically the spectrum of incidence matrices of random labeled
graphs on N vertices: any pair of vertices is connected by an edge with probability p. We …

We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency
matrices of sparse regular random graphs. We find that when the degree sequence of the …

We analyze the convergence of the spectrum of large random graphs to the spectrum of a
limit infinite graph. We apply these results to graphs converging locally to trees and derive a …

We carry out a numerical study of fluctuations in the spectra of regular graphs. Our
experiments indicate that the level spacing distribution of a generic k-regular graph …

We consider the ensemble of adjacency matrices of Erdős–Rényi random graphs, that is,
graphs on N vertices where every edge is chosen independently and with probability …

In this paper, we investigate the spectral properties of the adjacency and the Laplacian
matrices of random graphs. We prove that:(i) the law of large numbers for the spectral norms …