English Dictionary

medial graph

名詞

(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”.

日本語の意味

与えられた平面グラフから派生したグラフ。具体的には、元のグラフの各辺に1つの頂点が対応し、元のグラフの各面の境界上の連続する【辺・頂点・辺】の組（角）に対して、その角に関係する2つの辺に対応した頂点同士を結ぶ辺を持つグラフ。

To analyze face adjacency properties, the researcher constructed the medial graph of the planar embedding and examined how its vertices correspond to edges of the original graph.

面の隣接性を解析するため、研究者は元の平面グラフの各辺に対応する頂点をもち、面の境界に沿う“角”を構成する二つの辺に対応する頂点同士を結ぶようなグラフを構成し、それらの対応関係を調べた。

意味（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.

medial graphs （ plural ）