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Definitions of dual graph:
  • noun:   (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.

(Definitions from Wiktionary)

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