transitive closure


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


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 2 September 2014.
HTML page formatted Tue Feb 12 10:57:43 2019.

Cite this as:
Sandeep Kumar Shukla, "transitive closure", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 2 September 2014. (accessed TODAY) Available from: