transitive reduction

(definition)

Definition: The transitive reduction of a directed graph G is the directed graph G' with the smallest number of edges such that for every path between vertices in G, G' has a path between those vertices.

See also reduced digraph, transitive closure.

Note: Informally G' is the minimal graph with the same connectivity as G. After abstract of A. V. Aho, M. R. Garey, and J. D. Ullman. The transitive reduction of a directed graph. SIAM Journal on Computing, 1:131--137, 1972.

Author: PEB

Implementation

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 2 November 2020.
HTML page formatted Mon Nov 2 12:36:42 2020.

Cite this as:
Paul E. Black, "transitive reduction", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 2 November 2020. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/transitiveReduction.html