Discrete & Computational Geometry

, Volume 17, Issue 3, pp 263–282

On Nearest-Neighbor Graphs


DOI: 10.1007/PL00009293

Cite this article as:
Eppstein, D., Paterson, M.S. & Yao, F.F. Discrete Comput Geom (1997) 17: 263. doi:10.1007/PL00009293


The “nearest-neighbor” relation, or more generally the “k-nearest-neighbors” relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis, yet surprisingly little is known about some of its basic properties. In this paper we consider some natural questions that are motivated by geometric embedding problems. We derive bounds on the relationship between size and depth for the components of a nearest-neighbor graph and prove some probabilistic properties of the k-nearest-neighbors graph for a random set of points.

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  1. 1.Department of Information and Computer ScienceUniversity of CaliforniaIrvineUSA
  2. 2.Department of Computer ScienceUniversity of WarwickCoventryEngland
  3. 3.Xerox Palo Alto Research CenterPalo AltoUSA