BUILT-IN MATHEMATICA SYMBOL

# 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.

## Details and OptionsDetails 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

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Find a smallest edge cut:

 Out[2]=

Highlight an edge cut:

 Out[3]=

Find a smallest edge cut between two vertices:

 Out[1]=

### Properties & Relations (4)Properties & Relations (4)

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