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Discrete small world networks


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.

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®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:15 December 2006
Deposited On:16 Nov 2009 20:56
Last Modified:05 Apr 2016 13:23
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
Official URL:http://www.emis.de/journals/EJP-ECP/_ejpecp/viewarticle7f1a.html?id=1660
Related URLs:http://www.math.washington.edu/~ejpecp/
http://arxiv.org/abs/cond-mat/0304020
Permanent URL: https://doi.org/10.5167/uzh-21593

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