Digraph Representation of Binary Relation

Subjects to be Learned


A binary relation on a set can be represented by a digraph. Let R be a binary relation on a set A, that is R is a subset of A A. Then a digraph representing R can be constructed as follows:
Let the elements of A be the vertices of the digraph G, and let <x, y> be an arc of G from vertex x to vertex y if and only if <x, y> is in R.

Example: The less than relation R on the set of integers A = {1, 2, 3, 4} is the set {<1, 2> , <1, 3>, <1, 4>, <2, 3> , <2, 4> , <3, 4> } and it can be represented by the following digraph.

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