# 1.2 Directed Graph

If the edges of $G$ are ordered pairs, then $G$ is a directed graph. In a directed graph, $(v,w)\neq(w,v)$.

A directed graph is often referred to as a digraph. If edge $e$ of a digraph is represented by $(v,w)$, then $e$ is an edge from $v$ to $w$. Vertex $w$ is adjacent to vertex $v$. Vertex $v$ is not adjacent to vertex $w$ unless the edge $(w,v)$ also exists in $G$. The number of vertices adjacent to vertex $v$ is the degree of $v$. In-degree indicates the number of edges incident upon $v$. Out-degree indicates the number of edges emanating from $v$.

Figure 1 depicts a directed graph with six vertices and ten edges. In the figure, the arrowheads indicate the direction of the edge.

Vertex | Degree | In-Degree | Out-Degree |

1 | 2 | 1 | 1 |

2 | 4 | 1 | 3 |

3 | 4 | 2 | 2 |

4 | 4 | 3 | 1 |

5 | 3 | 2 | 1 |

6 | 3 | 1 | 2 |