Topic summary
Euclidean graph
Extracted from the Wikipedia article Geometric graph theory.
Different types of geometric graphs
A Euclidean graph is a graph in which the vertices represent points in the plane, and each edge is assigned the length equal to the Euclidean distance between its endpoints. The Euclidean minimum spanning tree is the minimum spanning tree of a Euclidean complete graph. It is also possible to define graphs by conditions on the distances; in particular, a unit distance graph is formed by connecting pairs of points that are a unit distance apart in the plane. The Hadwiger–Nelson problem concerns the chromatic number of these graphs.