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

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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

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

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

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Zentralblatt MATH identifier

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

preferential attachment stochastic approximation social networks competing types

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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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