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2014 The power of choice combined with preferential attachement
Yury Malyshkin, Elliot Paquette
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Electron. Commun. Probab. 19: 1-13 (2014). DOI: 10.1214/ECP.v19-3461


We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible neighbors are sampled from the existing vertices with probability proportional to degree. Of these possibilities, the new vertex attaches to the vertex from the sample that has the highest degree. The maximal degree in this model has linear or near-linear behavior. This behavior contrasts sharply with the behavior in the same choice model with uniform attachment as well as the preferential attachment model without choice. The proof is based on showing the tree has a persistent hub by comparison with the standard preferential attachment model, as well as martingale and stochastic approximation arguments.


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Yury Malyshkin. Elliot Paquette. "The power of choice combined with preferential attachement." Electron. Commun. Probab. 19 1 - 13, 2014.


Accepted: 12 July 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1298.05287
MathSciNet: MR3233206
Digital Object Identifier: 10.1214/ECP.v19-3461

Primary: 05C80

Keywords: choice , preferential attachment , stochastic approximation


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