# strongly connected graph

(definition)

**Definition:**
A *directed graph* that has a *path* from each *vertex* to every other vertex.

**Formal Definition:** A *directed graph* D=(V, E) such that for all pairs of *vertices* u, v ∈ V, there is a *path* from u to v and from v to u.

**See also**
*connected graph*, *strongly connected component*, *bridge*.

*Note:
From Algorithms and Theory of Computation Handbook, page 6-21, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.*

Author: CRC-A

## Implementation

(C++, 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 15 July 2019.

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

Cite this as:

Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "strongly connected graph", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 15 July 2019. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/stronglyConnectedGraph.html