Electronic Journal of Probability

High-Dimensional Random Geometric Graphs and their Clique Number

Luc Devroye, András György, Gábor Lugosi, and Frederic Udina

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We study the behavior of random geometric graphs in high dimensions. We show that as the dimension grows, the graph becomes similar to an Erdös-Rényi random graph. We pay particular attention to the clique number of such graphs and show that it is very close to that of the corresponding Erdös-Rényi graph when the dimension is larger than $\log^3(n)$ where $n$ is the number of vertices. The problem is motivated by a statistical problem of testing dependencies.

Article information

Electron. J. Probab. Volume 16 (2011), paper no. 90, 2481-2508.

Accepted: 30 November 2011
First available in Project Euclid: 1 June 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]
Secondary: 62H15: Hypothesis testing

Clique number dependency testing geometric graphs random graphs

This work is licensed under a Creative Commons Attribution 3.0 License.


Devroye, Luc; György, András; Lugosi, Gábor; Udina, Frederic. High-Dimensional Random Geometric Graphs and their Clique Number. Electron. J. Probab. 16 (2011), paper no. 90, 2481--2508. doi:10.1214/EJP.v16-967. http://projecteuclid.org/euclid.ejp/1464820259.

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