Open Access
2006 Discrete small world networks
Andrew Barbour, Gesine Reinert
Author Affiliations +
Electron. J. Probab. 11: 1234-1283 (2006). DOI: 10.1214/EJP.v11-381


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.


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Andrew Barbour. Gesine Reinert. "Discrete small world networks." Electron. J. Probab. 11 1234 - 1283, 2006.


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

zbMATH: 1184.90027
MathSciNet: MR2268544
Digital Object Identifier: 10.1214/EJP.v11-381

Primary: 90B15
Secondary: 60J85

Keywords: branching process , shortest path length , Small-world networks

Vol.11 • 2006
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