Andrews, B. and Jordan, J. orcid.org/0000-0003-4686-5440 (2021) Fragility of nonconvergence in preferential attachment graphs with three types. Involve, 14 (3). pp. 531-540. ISSN 1944-4176
Abstract
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2021 Mathematical Sciences Publishers. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | preferential attachment; competing types; rock-paper-scissors |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 Jul 2021 06:44 |
Last Modified: | 10 Aug 2021 07:05 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers |
Refereed: | Yes |
Identification Number: | 10.2140/involve.2021.14.531 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:176662 |