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In graph theory, multiple edges (also called parallel edges or a multi-edge), are two or more edges that are incident to the same two vertices. A simple graph has no multiple edges. Depending on the context, a graph may be defined so as to either allow or disallow the presence of multiple edges (often in concert with allowing or disallowing loops): *Where graphs are defined so as to ''allow'' multiple edges and loops, a graph without loops is often called a multigraph.〔For example, see Balakrishnan, p. 1, and Gross (2003), p. 4, Zwillinger, p. 220.〕 *Where graphs are defined so as to ''disallow'' multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which ''can'' have loops and multiple edges.〔For example, see Bollobás, p. 7, Diestel, p. 25, and Harary, p. 10.〕 Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view.〔Bollobás, pp. 39, 40.〕 Additionally, they constitute the core differentiating feature of multidimensional networks. A planar graph remains planar if an edge is added between two vertices already joined by an edge; thus, adding multiple edges preserves planarity.〔Gross (1998), p. 308.〕 A dipole graph is a graph with two vertices, in which all edges are parallel to each other. == Notes== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multiple edges」の詳細全文を読む スポンサード リンク
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