medial graph

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medial graph

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medial graph (plural medial graphs)

1. (graph theory) A graph derived from a given plane graph such that this derived graph has a vertex corresponding to each edge of the given graph, and such that for every “angle” (consecutive trio of edge, vertex, edge) along the border of a face of the given graph there is a corresponding edge which connects the vertices corresponding to the two edges that are part of that “angle”.

   The number of vertices of a medial graph is equal to the number of edges of its original graph, and the number of edges of a medial graph is equal to the sum of the degrees of the vertices of the original graph.

• plane graph
• regular graph