2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113920We show that almost surely the rank of the adjacency matrix of the Erdös-Rényi random graph $G(n,p)$ equals the number of non-isolated vertices for any $c\ln n/n<p<1/2$, where $c$ is an arbitrary positive constant larger than 1/2. In particular, the giant component (a.s.) has full rank in this range.19 pages, no figuresProbabilityCombinatorics15A52text