Advances in Applied Probability

Small-world graphs: characterization and alternative constructions

Rama Cont and Emily Tanimura

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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 the graph, which does not rely on any particular construction. Our definition is shown to encompass existing models of small-world graphs, proposed by Watts (1999) and studied by Barbour and Reinert (2001), 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.

Article information

Source
Adv. in Appl. Probab. Volume 40, Number 4 (2008), 939-965.

Dates
First available in Project Euclid: 7 January 2009

Permanent link to this document
http://projecteuclid.org/euclid.aap/1231340159

Digital Object Identifier
doi:10.1239/aap/1231340159

Mathematical Reviews number (MathSciNet)
MR2488527

Zentralblatt MATH identifier
1172.05050

Subjects
Primary: 05C80: Random graphs [See also 60B20]

Keywords
Random graph small-world model

Citation

Cont, Rama; Tanimura, Emily. Small-world graphs: characterization and alternative constructions. Adv. in Appl. Probab. 40 (2008), no. 4, 939--965. doi:10.1239/aap/1231340159. http://projecteuclid.org/euclid.aap/1231340159.


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