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++). Steven Skiena's Algorist/Stony Brook summary and links to implementations (C++, Java, 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 12 August 2019.
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Cite this as:
Sandeep Kumar Shukla, "transitive closure", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 12 August 2019. (accessed TODAY) Available from: