2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154660We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple proof of a recent result by van den Esker, van der Hofstad and Hooghiemstra on the equivalence between graph distances for some random graph models.21 pagesProbabilityCombinatorics60G30; 05C80; 60C05text