Haslegrave, J., Jordan, J. and Yarrow, M. (2020) Condensation in preferential attachment models with location-based choice. Random Structures and Algorithms, 56 (3). pp. 775-795. ISSN 1042-9832
Abstract
We introduce a new model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex in our model has an associated uniform random variable which we refer to as its location. Our model evolves in discrete time by selecting r vertices from the graph with replacement, with sampling probabilities proportional to their degrees plus a constant α. A new vertex joins the network and attaches to one of these r vertices according to a given probability associated to the ranking of their locations. Using stochastic approximation techniques we give conditions for the occurrence of condensation in this model, showing the existence of phase transitions in α below which condensation occurs. The condensation in our model differs from that in preferential attachment models with fitness in that the condensation can occur at a random location, that it can (but not necessarily) be due to a persistent hub, and that there can be more than one point of condensation.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Wiley Periodicals, Inc. This is an author-produced version of a paper subsequently published in Random Structures and Algorithms. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Preferential Attachment; Fitness; Location; Random Graphs; Phase Transition |
Dates: |
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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: | 24 Jun 2019 09:28 |
Last Modified: | 03 Dec 2021 14:35 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/rsa.20889 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:146779 |