dual graph

dual graph (plural dual graphs)

1. (graph theory) A graph derived from some plane graph in such a way that the derived graph has a vertex corresponding to each face of the given graph, an edge corresponding to each edge of the given graph that is shared by a pair of distinct faces, and a self-loop for each edge of the given graph that is a border of the same face on both of its sides.

   The edges of a dual graph are perpendicular, in some sense, to the edges of its original graph. The dual graph also has as many vertices and faces as its original graph has faces and vertices, respectively. Therefore the dual graph has the same Euler characteristic as its original graph.