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.
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Entry modified 3 November 2010.
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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. 3 November 2010. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/transitiveReduction.html