Projects per year
Abstract
We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent τ>2 . The average clustering coefficient of the networks converges to a positive limit. Finally, a phase transition occurs in the global clustering coefficients and empirical distribution of edge lengths when the power-law exponent crosses the critical value τ=3 . Our main tool in the proof of these results is a general weak law of large numbers in the spirit of Penrose and Yukich.
Original language | English |
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Pages (from-to) | 632-662 |
Number of pages | 31 |
Journal | Annals of Applied Probability |
Volume | 25 |
Issue number | 2 |
Early online date | 19 Feb 2015 |
DOIs | |
Publication status | Published - 31 Mar 2015 |
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Dive into the research topics of 'Spatial preferential attachment networks: Power laws and clustering coefficients'. Together they form a unique fingerprint.Projects
- 2 Finished
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Emergence of Condensation in Stochastic Systems
Morters, P.
Engineering and Physical Sciences Research Council
1/08/13 → 31/08/16
Project: Research council
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INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA
Morters, P.
Engineering and Physical Sciences Research Council
1/09/05 → 31/08/10
Project: Research council