Moment-Based Spectral Analysis of Random Graphs with Given Expected Degrees

We analyze the eigenvalues of a random graph ensemble, proposed by Chung and Lu, in which a given sequence of expected degrees, denoted by $\overline{w}_n = (w^{(n)}_1,\ldots, w^{(n)}_n)$ , is prescribed on the $n$ nodes of a random graph. We focus on the eigenvalues of the normalized (random) adjacency matrix of the graph ensemble, defined as $\mathbf {A}_n$ $=$ $\sqrt{n\rho _n}[\mathbf {a}^{...