Electronic Communications in Probability

Random walk attachment graphs

Chris Cannings and Jonathan Jordan

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We consider the random walk attachment graph introduced by Saramäki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge.  We show that if the length of the random walk is fixed then the resulting graphs can have properties significantly different from those of preferential attachment graphs, and in particular that in the case where the random walks are of length 1 and each new vertex attaches to a single existing vertex the proportion of vertices which have degree 1 tends to 1, in contrast to preferential attachment models.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 77, 5 pp.

Accepted: 18 September 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C82: Small world graphs, complex networks [See also 90Bxx, 91D30]

random graphs preferential attachment random walk

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


Cannings, Chris; Jordan, Jonathan. Random walk attachment graphs. Electron. Commun. Probab. 18 (2013), paper no. 77, 5 pp. doi:10.1214/ECP.v18-2518. https://projecteuclid.org/euclid.ecp/1465315616

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