The connectivity of a graph on uniform points on [0,\,1]\(^{d}\).
The authors compute the asymptotic behavior of the smallest value for which a class of uniformly distributed random graphs is connected. The connectivity of the random graph turns out to be equivalent, asymptotically, to its lack of isolated vertices. Hence, in dimension more than 2, the random graph of Appel and Russo behaves like random graph models of Erdős and Renyi.
scientific article; zbMATH DE number 1907011