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Mixed graph : ウィキペディア英語版
Mixed graph

A mixed graph ''G'' = (''V'', ''E'', ''A'') is a mathematical object consisting of a set of vertices (or nodes) ''V'', a set of (undirected) edges ''E'', and a set of directed edges (or arcs) ''A''.
==Definitions and Notation==

Consider adjacent vertices u,v \in V. A directed edge, called an arc, is an edge with an orientation and can be denoted as \overrightarrow or (u,v) (note that u is the tail and v is the head of the arc). Also, an undirected edge, or edge, is an edge with no orientation and can be denoted as uv or ().〔

For the purpose of our application example we will not be considering loops or multiple edges of mixed graphs.
A cycle of a mixed graph, or mixed cycle, is formed if the directed edges of the mixed graph form a cycle.〔 An orientation of a mixed graph is considered acyclic if cycles cannot be formed from the directed edges.〔 We call a mixed graph acyclic if all of its orientations are acyclic.〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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