Duality in inhomogeneous random graphs, and the cut metric

Details Duality in inhomogeneous random graphs, and the cut metric Duality in inhomogeneous random graphs, and the cut metric

2009-05-04

arxiv.org/abs/0905.0434v1

Random Structures and Algorithms 39 (2011) 399-411

Mathematics

Combinatorics

13 pages

Scientific paper

10.1002/rsa.20348

The classical random graph model $G(n,\lambda/n)$ 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.

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