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Haslegrave, J., Jordan, J. orcid.org/0000-0003-4686-5440 and Yarrow, M. orcid.org/0000-0002-4166-8037 (Submitted: 2018) Condensation in preferential attachment models with location-based choice. [Preprint - arXiv] (Submitted)
Abstract
We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model evolves in discrete time by selecting vertices from the graph with replacement, with probabilities proportional to their degrees plus a constant . A new vertex joins the network and attaches to one of these vertices according to a given probability associated to the ranking of their locations. We give conditions for the occurrence of condensation, showing the existence of phase transitions in 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 be due to a persistent hub, and that there can be more than one point of condensation.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 The Author(s). For reuse permissions, please contact the Author(s). |
Keywords: | Applied Mathematics; Mathematical Sciences |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 02 Jun 2025 15:08 |
Last Modified: | 02 Jun 2025 15:16 |
Status: | Submitted |
Identification Number: | 10.48550/arxiv.1806.10959 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:227292 |
Available Versions of this Item
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