Topics: Discrete Mathematics - Relation - Graph
(definition)
A digraph is a graph where all of its edges are directed (i.e. they are all arcs).
There are several types of digraphs (🗺).
Digraphs and Relations
We can graphically represent a given a relation in with a digraph.
A digraph is made out of the following elements:
- Vertices: each vertex is an element of
- Arcs: if , an arc is drawn from the vertex of to the vertex of
- If , then we draw a curved arc from to itself; we call this a loop.
We can use digraphs to easily determine the properties of the relation.
Example
For instance, let and be defined by if , .
Represented as a set, this relation is:
…and has the digraph:
