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April 2015 Spatial preferential attachment networks: Power laws and clustering coefficients
Emmanuel Jacob, Peter Mörters
Ann. Appl. Probab. 25(2): 632-662 (April 2015). DOI: 10.1214/14-AAP1006

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 $\tau>2$. 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 $\tau=3$. Our main tool in the proof of these results is a general weak law of large numbers in the spirit of Penrose and Yukich.

Citation

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Emmanuel Jacob. Peter Mörters. "Spatial preferential attachment networks: Power laws and clustering coefficients." Ann. Appl. Probab. 25 (2) 632 - 662, April 2015. https://doi.org/10.1214/14-AAP1006

Information

Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1310.05185
MathSciNet: MR3313751
Digital Object Identifier: 10.1214/14-AAP1006

Subjects:
Primary: 05C80
Secondary: 60C05, 90B15

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 2015
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