(definition)

**Definition:**
A *binary relation* R for which a R b implies b R a.

**See also**
*reflexive*, *transitive*, *antisymmetric*.

*Note:
The relation "not equal to" is symmetric: if a ≠ b, then b ≠ a. However, "loves" is not symmetric since love might not be reciprocated. The relation "is married to" is symmetric, but not antisymmetric: if Paul is married to Marlena, then Marlena is married to Paul (symmetric), but that does not mean that Paul and Marlena are the same person.*

Author: PEB

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Entry modified 17 December 2004.

HTML page formatted Mon Feb 2 13:10:40 2015.

Cite this as:

Paul E. Black, "symmetric", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/symmetric.html