This paper studies the asymptotic behaviors of the pairwise angles among n randomly and
uniformly distributed unit vectors in Rp as the number of points n→∞, while the dimension p …

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 …

Abstract The Random Geometric Graph (RGG) is a random graph model for network data
with an underlying spatial representation. Geometry endows RGGs with a rich dependence …

In this paper we study the random geometric graph $\mathsf {RGG}(n,\mathbb {T}^ d,\mathsf
{Unif},\sigma^ q_p, p) $ with $ L_q $ distance where each vertex is sampled uniformly from …

The random geometric graph model GRG d (n, p) is a distribution over graphs in which the
edges capture a latent geometry. To sample G∼ GRG d (n, p), we identify each of our n …

In the past decade, geometric network models have received vast attention in the literature.
These models formalize the natural idea that similar vertices are likely to connect. Because …

Random graphs with latent geometric structure are popular models of social and biological
networks, with applications ranging from network user profiling to circuit design. These …

Applications of machine learning methods increasingly deal with graph structured data
through kernels. Most existing graph kernels compare graphs in terms of features defined on …

Consider a random geometric 2-dimensional simplicial complex X sampled as follows: first,
sample n vectors u 1,…, un uniformly at random on S d− 1; then, for each triple i, j, k∈[n] …

We study the problem of detecting latent geometric structure in random graphs. To this end,
we consider the soft high-dimensional random geometric graph G (n, p, d, q), where each of …