Dual graph
![The red graph is the dual graph of the blue graph.](/Images/godic/202501/10/Duals_graphs.svg4938.png")
![The cube and regular octahedron have dual graphs](/Images/godic/202501/10/Dual_Cube-Octahedron.svg4938.png")
![A self-dual graph. It is 3-edge-connected (dual to being simple) but not 3-vertex-connected.](/Images/godic/202501/10/Self-dual_graph.svg4938.png")
![A Voronoi diagram (red) and Delaunay triangulation (black) of a finite point set (the black points)](/Images/godic/202501/10/Delaunay_Voronoi4938.png")
In the mathematical discipline of graph theory, the dual graph of a plane graph G is a graph that has a vertex for each face of G. The dual graph has an edge whenever two faces of G are separated from each other by an edge. Thus, each edge e of G has a corresponding dual edge, the edge that connects the two faces on either side of e.