(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
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 21 March 2005.
HTML page formatted Wed Feb 4 11:02:23 2009.
Cite this as:
Paul E. Black, "transitive reduction", in
Dictionary of Algorithms and Data
Structures [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 21 March 2005. (accessed TODAY)
Available from: http://www.itl.nist.gov/div897/sqg/dads/HTML/transitiveReduction.html
