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The largest component in a subcritical random graph with a power law degree distribution
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2008 (English)In: The Annals of Applied Probability, ISSN 1050-5164, Vol. 18, no 4, 1651-1668 p.Article in journal (Refereed) Published
Abstract [en]

It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent y > , 3, the largest component is of order n 1 Ay- 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.

Place, publisher, year, edition, pages
2008. Vol. 18, no 4, 1651-1668 p.
Keyword [en]
subcritical random graph, largest component, power law, random multigraph, random multigraph with given vertex degrees
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-106269DOI: 10.1214/07-AAP490ISI: 000258418800014OAI: oai:DiVA.org:uu-106269DiVA: diva2:224362
Available from: 2009-06-17 Created: 2009-06-17 Last updated: 2009-10-08Bibliographically approved

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