(definition)

**Definition:**
A *relation* between exactly two items at a time, such as "greater than" (>), "not equal to" (≠), "proper subset of" (⊂), or "is connected to" (has an *edge* to) for *vertices* of a *graph*.

**Generalization** (I am a kind of ...)

*relation*.

**Specialization** (... is a kind of me.)

*dictionary*.

**See also**
*binary function*, *reflexive*, *symmetric*, *transitive*, *antisymmetric*, *irreflexive*.

*Note:
One may think of a binary relation as a binary function whose range is {true, false}. For example since 3 > 2, GreaterThan(3, 2) = true.*

Author: PEB

Vreda Pieterse's explanation of different representations of binary relations.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 12 February 2019.

HTML page formatted Tue Feb 12 10:57:42 2019.

Cite this as:

Paul E. Black, "binary relation", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 12 February 2019. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/binaryRelation.html