# Discrete small world networks - Zurich Open Repository and Archive

Barbour, A D; Reinert, G (2006). Discrete small world networks. Electronic Journal of Probability, 11(47):1234-1283.

## Abstract

Small world models are networks consisting of many local links and fewer long range shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution of typical inter-point network distances. We establish approximations to the distribution of the graph distance in a discrete ring network with extra random links, and compare the results to those for simpler models, in which the extra links have zero length and the ring is continuous.

## Abstract

Small world models are networks consisting of many local links and fewer long range shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution of typical inter-point network distances. We establish approximations to the distribution of the graph distance in a discrete ring network with extra random links, and compare the results to those for simpler models, in which the extra links have zero length and the ring is continuous.

## Citations

5 citations in Web of Science®
8 citations in Scopus®

Detailed statistics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 15 December 2006 16 Nov 2009 20:56 05 Apr 2016 13:23 Institute of Mathematical Statistics 1083-6489 http://www.emis.de/journals/EJP-ECP/_ejpecp/viewarticle7f1a.html?id=1660 http://www.math.washington.edu/~ejpecp/http://arxiv.org/abs/cond-mat/0304020

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