# FindEdgeCut

FindEdgeCut[g]

finds a smallest edge cut of the graph g.

FindEdgeCut[g,s,t]

finds a smallest s-t edge cut of the graph g.

FindEdgeCut[{vw,},]

uses rules vw to specify the graph g.

# Details and Options

• An edge cut of a graph g is a set of edges whose deletion from g disconnects g.
• The s-t edge cut is a list of edges who deletion from g disconnects g with s and t in two different connected components.
• For weighted graphs, FindEdgeCut gives an edge cut with the smallest sum of edge weights.
• For a disconnected graph, FindEdgeCut will return an empty list {}.
• The following option can be given:
•  EdgeWeight Automatic edge weight for each edge

# Examples

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## Basic Examples(2)

Find a smallest edge cut:

Highlight an edge cut:

Find a smallest edge cut between two vertices:

## Scope(8)

FindEdgeCut works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Find an s-t edge cut:

Use rules to specify the graph:

FindEdgeCut works with 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:

## Applications(1)

Find the smallest set of relations disconnecting two members in a friendship network of a karate club:

Highlight the result:

## Properties & Relations(4)

Use EdgeConnectivity to obtain the size of the edge cut:

Use FindMinimumCut to obtain a partition of vertices associated to the edge cut:

Deleting the edge cut disconnects the graph:

FindEdgeCut returns an empty list for a disconnected graph:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_findedgecut, author="Wolfram Research", title="{FindEdgeCut}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindEdgeCut.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_findedgecut, organization={Wolfram Research}, title={FindEdgeCut}, year={2015}, url={https://reference.wolfram.com/language/ref/FindEdgeCut.html}, note=[Accessed: 24-July-2024 ]}