Given a planar graph G with a particular planar embedding, a geometric dual graph and combinatorial dual graph can be defined. Whitney showed that these are equivalent for planar graphs (Fleischner 1973, Harary 1994. p. 115) so that one may speak of "the" dual graph G^*. The illustration above shows the process of constructing a geometric dual graph from a planar nonpolyhedral graph, leading to a multigraph.

combinatorial dual graph | geometric dual graph | planar graph | self-dual graph