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Condensation in preferential attachment models with location-based choice
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Haslegrave, John, Jordan, Jonathan and Yarrow, Mark (2020) Condensation in preferential attachment models with location-based choice. Random Structures and Algorithms, 56 (3). pp. 775-795. doi:10.1002/rsa.20889 ISSN 1042-9832.
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Official URL: https://doi.org/10.1002/rsa.20889
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 r vertices from the graph with replacement, with probabilities proportional to their degrees plus a constant α. 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 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 be due to a persistent hub, and that there can be more than one point of condensation.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Journal or Publication Title: | Random Structures and Algorithms | ||||||||
| Publisher: | John Wiley & Sons, Inc. | ||||||||
| ISSN: | 1042-9832 | ||||||||
| Official Date: | May 2020 | ||||||||
| Dates: |
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| Volume: | 56 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 775-795 | ||||||||
| DOI: | 10.1002/rsa.20889 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This is the peer reviewed version of the following article: Haslegrave, J, Jordan, J, Yarrow, M. Condensation in preferential attachment models with location‐based choice. Random Struct Alg. 2020; 56: 775– 795. https://doi.org/10.1002/rsa.20889. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 6 June 2019 | ||||||||
| Date of first compliant Open Access: | 2 October 2020 | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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