2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229181We 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 new formula for the Stieljes transform of the spectral measure of such graphs. We illustrate our results on the uniform regular graphs, Erdos-Renyi graphs and preferential attachment graphs. We sketch examples of application for weighted graphs, bipartite graphs and the uniform spanning tree of n vertices.21 pages, 1 figureProbabilityMathematical Physics05C80, 15A52 (Primary); 47A10 (Secondary)text