Testing for high‐dimensional geometry in random graphs

  title={Testing for high‐dimensional geometry in random graphs},
  author={S{\'e}bastien Bubeck and Jian Ding and Ronen Eldan and Mikl{\'o}s Z. R{\'a}cz},
  journal={Random Structures \& Algorithms},
We study the problem of detecting the presence of an underlying high‐dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erdős‐Rényi random graph G(n, p). Under the alternative, the graph is generated from the G(n,p,d) model, where each vertex corresponds to a latent independent random vector uniformly distributed on the sphere Sd−1 , and two vertices are connected if the corresponding latent vectors are close enough. In the… 
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