(definition)

**Definition:**
A *connected graph* such that deleting any k-1 *vertices* (and incident *edges*) results in a graph that is still connected.

**See also**
*biconnected graph*, *triconnected graph*, *cut vertex*.

*Note:
Informally, there are at least k independent paths from any vertex to any other vertex.*

Author: PMS

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Entry modified 19 April 2004.

HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:

Paul M. Sant, "k-connected graph", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 19 April 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/kconnectedGraph.html