High-dimensional random geometric graphs and their clique number ## AbstractWe study the behavior of random geometric graphs in high dimensions. We show that as the dimension grows, the graph becomes similar to an Erd ̋os-R ́enyi 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 Erd ̋os-R ́enyi graph when the dimension is larger than log3 n where n is the number of vertices. The problem is motivated by a statistical problem of testing dependencies.
[Edit] |