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.
Citation
Luc Devroye. András György. Gábor Lugosi. Frederic Udina. "High-Dimensional Random Geometric Graphs and their Clique Number." Electron. J. Probab. 16 2481 - 2508, 2011. https://doi.org/10.1214/EJP.v16-967
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