NIST

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

on a graph (C++ and Mathematica)
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Entry modified 2 September 2014.
HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:
Paul E. Black, "transitive reduction", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 2 September 2014. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/transitiveReduction.html