The largest component in a subcritical random graph with a power law degree distribution

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dc.creatorJanson, Svante
dc.date2007-08-31
dc.date2008-08-21
dc.date.accessioned2026-07-07T09:57:24Z
dc.date.available2026-07-07T09:57:24Z
dc.descriptionIt 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.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/0708.4404
dc.identifierhttp://arxiv.org/abs/0708.4404
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 4, 1651-1668
dc.identifierdoi:10.1214/07-AAP490
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167326
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60C05, 05C80 (Primary)
dc.titleThe largest component in a subcritical random graph with a power law degree distribution
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