Electronic Communications in Probability

Non-convergence of proportions of types in a preferential attachment graph with three co-existing types

John Haslegrave and Jonathan Jordan

Full-text: Open access

Abstract

We consider the preferential attachment model with multiple vertex types introduced by Antunović, Mossel and Rácz. We give an example with three types, based on the game of rock-paper-scissors, where the proportions of vertices of the different types almost surely do not converge to a limit, giving a counterexample to a conjecture of Antunović, Mossel and Rácz. We also consider another family of examples where we show that the conjecture does hold.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 54, 12 pp.

Dates
Received: 29 May 2018
Accepted: 25 July 2018
First available in Project Euclid: 1 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1535767265

Digital Object Identifier
doi:10.1214/18-ECP157

Mathematical Reviews number (MathSciNet)
MR3852268

Zentralblatt MATH identifier
1398.05187

Subjects
Primary: 05C82: Small world graphs, complex networks [See also 90Bxx, 91D30]
Secondary: 05C80: Random graphs [See also 60B20] 60C05: Combinatorial probability 90B15: Network models, stochastic

Keywords
preferential attachment stochastic approximation social networks competing types

Rights
Creative Commons Attribution 4.0 International License.

Citation

Haslegrave, John; Jordan, Jonathan. Non-convergence of proportions of types in a preferential attachment graph with three co-existing types. Electron. Commun. Probab. 23 (2018), paper no. 54, 12 pp. doi:10.1214/18-ECP157. https://projecteuclid.org/euclid.ecp/1535767265


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References

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