Electronic Journal of Probability

Discrete small world networks

Andrew Barbour and Gesine Reinert

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Small-world networks shortest path length branching process

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


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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