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# edgeCuts -- returns the edge cuts of a graph

- Usage:
    `C = edgeCuts G`
- Inputs:
  - G, a graph,
- Outputs:
  - C, a list, the edge cuts of a graph

## Description

An edge cut is a minimal set of edges that, when removed from a graph, make the graph not connected. If the graph is already not connected, the method returns the empty set.

    i1 : G = graph({{1,2},{2,3},{3,1},{3,4},{4,5},{5,3}},EntryMode=>"edges");

    i2 : edgeCuts G

    o2 = {{{1, 2}, {1, 3}}, {{1, 2}, {2, 3}}, {{1, 3}, {2, 3}}, {{4, 3}, {5, 3}},
         ------------------------------------------------------------------------
         {{4, 3}, {4, 5}}, {{5, 3}, {4, 5}}}

    o2 : List

## See also

- vertexCuts -- lists all the vertex cuts of a graph
- minimalVertexCuts -- finds the minimal vertex cuts of a graph
- edgeConnectivity -- computes the edge connectivity of a graph

## Ways to use edgeCuts:

- `edgeCuts(Graph)`

## For the programmer

The object edgeCuts is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Graphs.m2:2909:0.