Open Access
2013 Geometric preferential attachment in non-uniform metric spaces
Jonathan Jordan
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Electron. J. Probab. 18: 1-15 (2013). DOI: 10.1214/EJP.v18-2271


We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that of the preferential attachment with multiplicative fitness models investigated by Borgs et al. When the metric space is finite, the degree distribution at each point of the space converges to a degree distribution which is an asymptotic power law whose index depends on the chosen point. For infinite metric spaces, we can show that for vertices in a Borel subset of <em>S</em> of positive measure the degree distribution converges to a distribution whose tail is close to that of a power law whose index again depends on the set.


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Jonathan Jordan. "Geometric preferential attachment in non-uniform metric spaces." Electron. J. Probab. 18 1 - 15, 2013.


Accepted: 14 January 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1283.05249
MathSciNet: MR3024102
Digital Object Identifier: 10.1214/EJP.v18-2271

Primary: 05C82
Secondary: 60D05

Keywords: Geometric random graphs , preferential attachment

Vol.18 • 2013
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