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minimum_edge_cut(G, s=None, t=None, flow_func=None)

If source and target nodes are provided, this function returns the set of edges of minimum cardinality that, if removed, would break all paths among source and target in G. If not, it returns a set of edges of minimum cardinality that disconnects G.

Notes

This is a flow based implementation of minimum edge cut. For undirected graphs the algorithm works by finding a 'small' dominating set of nodes of G (see algorithm 7 in ) and computing the maximum flow between an arbitrary node in the dominating set and the rest of nodes in it. This is an implementation of algorithm 6 in . For directed graphs, the algorithm does n calls to the max flow function. The function raises an error if the directed graph is not weakly connected and returns an empty set if it is weakly connected. It is an implementation of algorithm 8 in .

Parameters

G : NetworkX graph
s : node

Source node. Optional. Default value: None.

t : node

Target node. Optional. Default value: None.

flow_func : function

A function for computing the maximum flow among a pair of nodes. The function has to accept at least three parameters: a Digraph, a source node, and a target node. And return a residual network that follows NetworkX conventions (see maximum_flow for details). If flow_func is None, the default maximum flow function ( edmonds_karp ) is used. See below for details. The choice of the default function may change from version to version and should not be relied on. Default value: None.

Returns

cutset : set

Set of edges that, if removed, would disconnect G. If source and target nodes are provided, the set contains the edges that if removed, would destroy all paths between source and target.

Returns a set of edges of minimum cardinality that disconnects G.

See Also

edge_connectivity

meth

edmonds_karp

meth

maximum_flow

meth

minimum_node_cut

meth

minimum_st_edge_cut

meth

node_connectivity

meth

preflow_push

meth

shortest_augmenting_path

meth

stoer_wagner

meth

Examples

>>> # Platonic icosahedral graph has edge connectivity 5
... G = nx.icosahedral_graph()
... len(nx.minimum_edge_cut(G)) 5

You can use alternative flow algorithms for the underlying maximum flow computation. In dense networks the algorithm shortest_augmenting_path will usually perform better than the default edmonds_karp , which is faster for sparse networks with highly skewed degree distributions. Alternative flow functions have to be explicitly imported from the flow package.

>>> from networkx.algorithms.flow import shortest_augmenting_path
... len(nx.minimum_edge_cut(G, flow_func=shortest_augmenting_path)) 5

If you specify a pair of nodes (source and target) as parameters, this function returns the value of local edge connectivity.

>>> nx.edge_connectivity(G, 3, 7)
5

If you need to perform several local computations among different pairs of nodes on the same graph, it is recommended that you reuse the data structures used in the maximum flow computations. See local_edge_connectivity for details.

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.connectivity.cuts.minimum_node_cut networkx.algorithms.connectivity.cuts.minimum_st_node_cut networkx.algorithms.connectivity.cuts.minimum_edge_cut networkx.algorithms.connectivity.cuts.minimum_st_edge_cut

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /networkx/algorithms/connectivity/cuts.py#439
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