Def/Digraph

Definition of Digraph: A digraph, short for directed graph, (with no multiple edges, but loops allowed) is an ordered pair $(V,E)$, consisting of the following data:

A drawing of the digraph: $V = \{ 1,2,3,4 \}$, $E= \{ (1,1), (2,3), (3,4)$, $(2,4), (3,1) \}$.

• $V$ is a set.
• $E$ is a subset of the Cartesian product $V \times V$.

Such data $(V,E)$ is meant to be considered visually as follows:

• The elements of $V$ are called vertices, or nodes of the digraph.
• If $s,t \in V$, and $(s,t) \in E$, then the ordered pair $(s,t)$ is called an edge of the digraph, directed from $s$ to $t$. Sometimes, $s$ is called the source, and $t$ the target of the edge $(s,t)$.