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2021 Fragility of nonconvergence in preferential attachment graphs with three types
Ben Andrews, Jonathan Jordan
Involve 14(3): 531-540 (2021). DOI: 10.2140/involve.2021.14.531


Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random and are more likely to connect to those that already have many connections. We investigate further a family of models introduced by Antunović, Mossel and Rácz where each vertex in a preferential attachment graph is assigned a type, based on the types of its neighbours. Instances of this type of process where the proportions of each type present do not converge over time seem to be rare.

Previous work found that a “rock-paper-scissors” setup where each new node’s type was determined by a rock-paper-scissors contest between its two neighbours does not converge. Here, two cases similar to that are considered, one which is like the above but with an arbitrarily small chance of picking a random type and one where there are four neighbours which perform a knockout tournament to determine the new type.

These two new setups, despite seeming very similar to the rock-paper-scissors model, do in fact converge, perhaps surprisingly.


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Ben Andrews. Jonathan Jordan. "Fragility of nonconvergence in preferential attachment graphs with three types." Involve 14 (3) 531 - 540, 2021.


Received: 2 February 2021; Accepted: 26 February 2021; Published: 2021
First available in Project Euclid: 30 July 2021

Digital Object Identifier: 10.2140/involve.2021.14.531

Primary: 05C82

Keywords: competing types , preferential attachment , rock-paper-scissors

Rights: Copyright © 2021 Mathematical Sciences Publishers


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Vol.14 • No. 3 • 2021
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