# vertex connectivity

(definition)

**Definition:**
(1) The smallest number of *vertices* whose deletion causes a *connected graph* to not be connected. (2) For a pair of vertices s and t in a graph, the smallest number of vertices whose deletion will separate s from t.

**See also**
*edge connectivity*.

Author: GS

## Implementation

Steve Skiena's Stony Brook Algorithm Repository (C, C++, Java, and Mathematica)

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Dictionary of Algorithms and Data
Structures home page.

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Entry modified 12 August 2019.

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

Cite this as:

Gopinath Srinivasan, "vertex connectivity", 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/vertexConnectivity.html