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.

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

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