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**Binary relations represented by directed graphs **

A binary relation can be represented by a *directed graph*. We can draw a directed links as arrows, from *a* to *b* for any two values *a* and *b* for which *aRb* is true. We can see this exemplified below in the examples of relations with the properties of the previous page.

The *reflexivity* holds if every element in a directed graph points to themselves. The graph below shows the relation “*b*=(*a+q*) mod 3 where *q*=0 or 1″ over the set {0,1,2}.

The graph will also be an example of *Antisymmetry*, where the only double directed arrows are the ones possibly directed from an element onto itself.

The *antireflexivity* holds if no element point to itself. The graph below shows the relation a*<b* over the set {0,1,2}.

The graph will also be an example of an *asymmetry* since we have no double directed relations.

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