Electronic Communications in Probability

Random walk attachment graphs

Chris Cannings and Jonathan Jordan

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315616

Digital Object Identifier
doi:10.1214/ECP.v18-2518

Mathematical Reviews number (MathSciNet)
MR3109632

Zentralblatt MATH identifier
1298.05289

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

Keywords
random graphs preferential attachment random walk

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

Citation

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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