Topics: Discrete Mathematics

Let be a relation and be its matrix.

We can use or the relation’s digraph to easily determine the properties of :

  1. Reflexive if and only if has s in its diagonal.
  2. Symmetric if and only if all arrows in the digraph are bidirectional.
  3. Antisymmetric if and only if between any two vertices there is, at least, one arrow.
  4. Transitive if and only if the digraph holds the property that if there exist arrows from to and from to , then there’s one from to .