February 2024 Collection: Preferential Attachment Networks
Preferential attachment networks were popularised by Barabási and Albert in the late 1990s as models for complex systems and realworld networks; examples suggested included social networks, the World Wide Web and biological networks. The key principle is that the probability that a vertex's probability of acquiring new connections increases with its existing connectivity, something which is a natural assumption when modelling many systems.
One of the first probabilistic results obtained on preferential attachment was that, as predicted by Barabási and Albert, the basic preferential attachment rule produces a distribution of vertex degrees which asymptotically follows a power law, something which has been claimed for many realworld systems. There has also been much interest in the structural properties of these graphs, for example their diameter and local structure.
Further developments have considered modifications of the basic model. Examples of such modifications include the introduction of vertex fitnesses, nonlinear relationships between connectivity and ability to attract new connections, geometric embeddings of the model, and versions which allow for vertices to be removed from the network as well as added. These developments are of interest for better modelling of some of the realworld systems which motivated the original work, but they also produce much interesting mathematics.
Collection created by Dr Jonathan Jordan (University of Sheffield)
Original Article
Local weak limit of preferential attachment random trees with additive fitness
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 Journal:
 Advances in Applied Probability , First View
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 19 January 2024, pp. 140

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Degree distributions in recursive trees with fitnesses
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 Advances in Applied Probability / Volume 55 / Issue 2 / June 2023
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 06 March 2023, pp. 407443

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Dynamical fitness models: evidence of universality classes for preferential attachment graphs
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 Journal of Applied Probability / Volume 59 / Issue 3 / 2022
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 21 June 2022, pp. 609630

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Preferential attachment when stable
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 Advances in Applied Probability / Volume 51 / Issue 4 / 2019
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 15 November 2019, pp. 10671108

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Subgraphs in preferential attachment models
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 Advances in Applied Probability / Volume 51 / Issue 3 / September 2019
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 03 September 2019, pp. 898926

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Research Article
Joint degree distributions of preferential attachment random graphs
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 Advances in Applied Probability / Volume 49 / Issue 2 / 2017
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 26 June 2017, pp. 368387

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Random Networks with Preferential Growth and Vertex Death
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 Journal of Applied Probability / Volume 47 / Issue 4 / December 2010
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 14 July 2016, pp. 11501163

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Research Papers
Nonstandard regular variation of indegree and outdegree in the preferential attachment model

 Journal:
 Journal of Applied Probability / Volume 53 / Issue 1 / March 2016
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 24 March 2016, pp. 146161

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Research Article
Phase Transitions for Random Geometric Preferential Attachment Graphs
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 Advances in Applied Probability / Volume 47 / Issue 2 / 2015
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 22 February 2016, pp. 565588

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General Applied Probability
Power Laws in Preferential Attachment Graphs and Stein's Method for the Negative Binomial Distribution
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 Journal:
 Advances in Applied Probability / Volume 45 / Issue 3 / 2013
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 04 January 2016, pp. 876893

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