Editing Voronoi diagram (section)

==Properties==
* The [[dual graph]] for a Voronoi diagram (in the case of a [[Euclidean space]] with point sites) corresponds to the [[Delaunay triangulation]] for the same set of points.
* The [[closest pair of points]] corresponds to two adjacent cells in the Voronoi diagram.
* If the setting is the [[Euclidean plane]] and a discrete set of points is given, then two points of the set are adjacent on the [[convex hull]] if and only if their Voronoi cells share an infinitely long side.
* If the space is a [[normed space]] and the distance to each site is attained (e.g., when a site is a [[compact set]] or a closed ball), then each Voronoi cell can be represented as a union of line segments emanating from the sites.<ref name=Reem_alg>{{harvnb|Reem|2009}}.</ref> As shown there, this property does not necessarily hold when the distance is not attained.
* Under relatively general conditions (the space is a possibly infinite-dimensional [[uniformly convex space]], there can be infinitely many sites of a general form, etc.) Voronoi cells enjoy a certain stability property: a small change in the shapes of the sites, e.g., a change caused by some translation or distortion, yields a small change in the shape of the Voronoi cells. This is the geometric stability of Voronoi diagrams.<ref name=Reem_geo_stable>{{harvnb|Reem|2011}}.</ref> As shown there, this property does not hold in general, even if the space is two-dimensional (but non-uniformly convex, and, in particular, non-Euclidean) and the sites are points.