Watts and Strogatz, with the publication in 1998 of their seminal paper on small-world
networks, opened the golden era of complex networks studies and showed in particular how …

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 …

Network models with latent geometry have been used successfully in many applications in
network science and other disciplines, yet it is usually impossible to tell if a given real …

Networks with underlying metric spaces attract increasing research attention in network
science, statistical physics, applied mathematics, computer science, sociology, and other …

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 …

Steady technological advances are paving the way for the implementation of the quantum
internet, a network of locations interconnected by quantum channels. Here we propose a …

We study continuum percolation with disks, a variant of continuum percolation in two-
dimensional Euclidean space, by applying tools from topological data analysis. We interpret …

In this paper, we study the connectivity of a one-dimensional soft random geometric graph
(RGG). The graph is generated by placing points at random on a bounded line segment and …

We study the emergence of a giant component in a spatial network where the nodes form a
fractal set, and the interaction between the nodes has a long-range power-law behavior. The …

In this work we perform a detailed statistical analysis of topological and spectral properties of
random geometric graphs (RGGs), a graph model used to study the structure and dynamics …