Directed graph

Definition

A directed graph, or digraph, is a pair $D = (V, A)$ of a set $V$ and a relation $A \subseteq V \times V$ . The elements of $V$ are the vertices of $D$ . The elements of $A$ are the arcs, or directed edges, of $D$ . An arc $(u, v)$ goes from its tail $u$ to its head $v$ .

Remarks

With this definition a digraph can have loops $(v, v)$ , and it has at most one arc from $u$ to $v$ . Some authors exclude loops. A graph is the same as a digraph whose relation is symmetric and irreflexive. The out-degree of $v$ is the number of arcs with tail $v$ , and the in-degree is the number of arcs with head $v$ .

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Tag	`0R5HTV7REV`
URI	`m2://0R5HTV7REV`
Kind	definition
Writing	W1 stated
MSC	05C20
Defines	Directed graph

Directed graph

Definition

Remarks

Where this leads

Further reading

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