# transitive closure

(definition)

**Definition:**
An extension or superset of a *binary relation* such that whenever (a,b) and (b,c) are in the extension, (a,c) is also in the extension.

**See also**
*transitive reduction*, *transitive*.

Author: SKS

## Implementation

Vreda Pieterse's explanation of binary relations and transitive closure with links to implementations (C++); Stony Brook's explanation and links to implementations (C++ and Mathematica).

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 28 July 2014.

HTML page formatted Mon Jul 28 16:27:59 2014.

Cite this as:

Sandeep Kumar Shukla, "transitive closure", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 28 July 2014. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/transitiveClosure.html