Electronic Journal of Probability

Discrete small world networks

Andrew Barbour and Gesine Reinert

Full-text: Open access

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.

Article information

Source
Electron. J. Probab. Volume 11 (2006), paper no. 47, 1234-1283.

Dates
Accepted: 15 December 2006
First available in Project Euclid: 31 May 2016

Permanent link to this document
http://projecteuclid.org/euclid.ejp/1464730582

Digital Object Identifier
doi:10.1214/EJP.v11-381

Mathematical Reviews number (MathSciNet)
MR2268544

Subjects
Primary: 90B15: Network models, stochastic
Secondary: 60J85: Applications of branching processes [See also 92Dxx]

Keywords
Small-world networks shortest path length branching process

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Barbour, Andrew; Reinert, Gesine. Discrete small world networks. Electron. J. Probab. 11 (2006), paper no. 47, 1234--1283. doi:10.1214/EJP.v11-381. http://projecteuclid.org/euclid.ejp/1464730582.


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