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Homedirected graph

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# directed graph

A *directed graph* or *digraph* is a pair $G=(V,E)$ where $V$ is a set of *vertices* and $E$ is a subset of $V\times V$ called *edges* or *arcs*.

If $E$ is symmetric (i.e., $(u,v)\in E$ if and only if $(v,u)\in E$), then the digraph is isomorphic to an ordinary (that is, undirected) graph.

Digraphs are generally drawn in a similar manner to graphs with arrows on the edges to indicate a sense of direction. For example, the digraph

$\left(\{a,b,c,d\},\{(a,b),(b,d),(b,c),(c,b),(c,c),(c,d)\}\right)$ |

may be drawn as

Defines:

in-degree, out-degree, directed spanning tree

Related:

Graph, VeblensTheorem, GraphTheory

Synonym:

digraph, in degree, out degree

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C20*no label found*

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