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Duality in Inhomogeneous Random Graphs, and the Cut Metric
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 39, no 3, 399-411 p.Article in journal (Refereed) Published
Abstract [en]

The classical random graph model G(n, c/n) satisfies a "duality principle", in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved for various models; they are useful since it is often much easier to study the subcritical model than to directly study small components in the supercritical model. Here we prove a duality principle of this type for a very general class of random graphs with independence between the edges, defined by convergence of the matrices of edge probabilities in the cut metric.

Place, publisher, year, edition, pages
2011. Vol. 39, no 3, 399-411 p.
Keyword [en]
cut metric, random graph duality
National Category
URN: urn:nbn:se:uu:diva-158565DOI: 10.1002/rsa.20348ISI: 000294266600004OAI: oai:DiVA.org:uu-158565DiVA: diva2:440578
Available from: 2011-09-13 Created: 2011-09-12 Last updated: 2012-02-16Bibliographically approved

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