# 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 2 November 2020.

HTML page formatted Mon Nov 2 12:36:42 2020.

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. 2 November 2020. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/stronglyConnectedGraph.html