# 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 12 August 2019.

HTML page formatted Mon Aug 12 09:59:40 2019.

Cite this as:

Paul E. Black, "transitive reduction", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 12 August 2019. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/transitiveReduction.html