VertexConnectivity[g]
gives the minimum number of vertices whose deletion from graph disconnects it.
VertexConnectivity[g,Cut]
gives a set of vertices of minimum size whose removal disconnects the graph.


VertexConnectivity
VertexConnectivity[g]
gives the minimum number of vertices whose deletion from graph disconnects it.
VertexConnectivity[g,Cut]
gives a set of vertices of minimum size whose removal disconnects the graph.
Details and Options
- VertexConnectivity functionality is now available in the built-in Wolfram Language function VertexConnectivity.
- To use VertexConnectivity, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
Tech Notes
Related Guides
-
▪
- Cycles and Connectivity ▪
- Graphs & Networks ▪
- Graph Visualization ▪
- Computation on Graphs ▪
- Graph Construction & Representation ▪
- Graphs and Matrices ▪
- Graph Properties & Measurements ▪
- Graph Operations and Modifications ▪
- Statistical Analysis ▪
- Social Network Analysis ▪
- Graph Properties ▪
- Mathematical Data Formats ▪
- Discrete Mathematics
Text
Wolfram Research (2012), VertexConnectivity, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/VertexConnectivity.html.
CMS
Wolfram Language. 2012. "VertexConnectivity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/VertexConnectivity.html.
APA
Wolfram Language. (2012). VertexConnectivity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/VertexConnectivity.html
BibTeX
@misc{reference.wolfram_2025_vertexconnectivity, author="Wolfram Research", title="{VertexConnectivity}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/VertexConnectivity.html}", note=[Accessed: 13-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_vertexconnectivity, organization={Wolfram Research}, title={VertexConnectivity}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/VertexConnectivity.html}, note=[Accessed: 13-August-2025]}