Small world graphs: characterization and alternative constructions

Abstract : Small world graphs are examples of random graphs which mimic empirically observed features of social networks. We propose an intrinsic definition of small world graphs, based on a probabilistic formulation of scaling properties of graph properties, which does not rely on an underlying lattice nor on any particular construction. Our definition is shown to encompass existing models of small world graphs, proposed by Watts and studied by Barbour & Reinert, which are based on random perturbations of a regular lattice. We also propose alternative constructions of small world graphs which are not based on lattices and study their scaling properties.
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Advances in Applied Probability, Applied Probability Trust, 2008, 40 (4), pp.939-965. <10.1239/aap/1231340159>
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Contributeur : Rama Cont <>
Soumis le : mercredi 21 octobre 2009 - 00:58:14
Dernière modification le : vendredi 28 avril 2017 - 01:02:46

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Rama Cont, Emily Tanimura. Small world graphs: characterization and alternative constructions. Advances in Applied Probability, Applied Probability Trust, 2008, 40 (4), pp.939-965. <10.1239/aap/1231340159>. <hal-00425341>

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