# EdgeConnectivity

gives the edge connectivity of the graph g.

EdgeConnectivity[g,s,t]

gives the s-t edge connectivity of the graph g.

EdgeConnectivity[{vw,},]

uses rules vw to specify the graph g.

# Details and Options

• EdgeConnectivity is also known as line connectivity.
• The edge connectivity of a graph g is the smallest number of edges whose deletion from g disconnects g.
• The s-t edge connectivity is the smallest number of edges whose deletion from g disconnects g, with s and t in two different connected components.
• For weighted graphs, EdgeConnectivity gives the smallest sum of edge weights.
• For a disconnected graph, EdgeConnectivity will return 0.
• The following option can be given:
•  EdgeWeight Automatic edge weight for each edge

# Examples

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## Basic Examples(2)

Find the edge connectivity:

Find the edge connectivity between two vertices:

## Scope(7)

EdgeConnectivity works on undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

EdgeConnectivity works on large graphs:

## Options(1)

### EdgeWeight(1)

By default, the edge weight of an edge is taken to be its EdgeWeight property if available, otherwise 1:

Use EdgeWeight->weights to set the edge weight:

## Properties & Relations(3)

Use FindEdgeCut to compute the edge connectivity:

The maximum flow between two vertices is equal to the edge connectivity:

EdgeConnectivity returns 0 for a disconnected graph:

Wolfram Research (2012), EdgeConnectivity, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeConnectivity.html (updated 2015).

#### Text

Wolfram Research (2012), EdgeConnectivity, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeConnectivity.html (updated 2015).

#### CMS

Wolfram Language. 2012. "EdgeConnectivity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/EdgeConnectivity.html.

#### APA

Wolfram Language. (2012). EdgeConnectivity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EdgeConnectivity.html

#### BibTeX

@misc{reference.wolfram_2024_edgeconnectivity, author="Wolfram Research", title="{EdgeConnectivity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/EdgeConnectivity.html}", note=[Accessed: 18-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_edgeconnectivity, organization={Wolfram Research}, title={EdgeConnectivity}, year={2015}, url={https://reference.wolfram.com/language/ref/EdgeConnectivity.html}, note=[Accessed: 18-July-2024 ]}