2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167326It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent $γ>3$, the largest component is of order $n^{1/(γ-1)}$. More precisely, the order of the largest component is approximatively given by a simple constant times the largest vertex degree. These results are extended to several other random graph models with power law degree distributions. This proves a conjecture by Durrett.Published in at http://dx.doi.org/10.1214/07-AAP490 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)ProbabilityCombinatorics60C05, 05C80 (Primary)text