medial graph

Noun

 * 1)  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 &ldquo;angle&rdquo; (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 &ldquo;angle&rdquo;.
 * 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.

Hypernyms

 * plane graph
 * regular graph