# 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