Abstract:If (ω(e)) is a family of random variables (weights) assigned to the edges of Z d , the nearest neighbor graph is the directed graph induced by all edges x, y such that ω({x, y}) is minimal among all neighbors y of x. That is, each vertex points to its closest neighbor, if the weights are viewed as edge-lengths. Nanda-Newman introduced nearest neighbor graphs when the weights are i.i.d. and continuously distributed and proved that a.s., all components of the undirected version of the graph are finite. We study … Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.