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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820259

Digital Object Identifier
doi:10.1214/EJP.v16-967

Mathematical Reviews number (MathSciNet)
MR2861682

Zentralblatt MATH identifier
1244.05200

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

Keywords
Clique number dependency testing geometric graphs random graphs

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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. https://projecteuclid.org/euclid.ejp/1464820259


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