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minimum_st_edge_cut(G, s, t, flow_func=None, auxiliary=None, residual=None)

This function returns the set of edges of minimum cardinality that, if removed, would destroy all paths among source and target in G. Edge weights are not considered. See minimum_cut for computing minimum cuts considering edge weights.

Parameters

G : NetworkX graph
s : node

Source node for the flow.

t : node

Sink node for the flow.

auxiliary : NetworkX DiGraph

Auxiliary digraph to compute flow based node connectivity. It has to have a graph attribute called mapping with a dictionary mapping node names in G and in the auxiliary digraph. If provided it will be reused instead of recreated. 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 node_connectivity for details. The choice of the default function may change from version to version and should not be relied on. Default value: None.

residual : NetworkX DiGraph

Residual network to compute maximum flow. If provided it will be reused instead of recreated. Default value: None.

Returns

cutset : set

Set of edges that, if removed from the graph, will disconnect it.

Returns the edges of the cut-set of a minimum (s, t)-cut.

See Also

edge_connectivity

meth

edmonds_karp

meth

maximum_flow

meth

minimum_cut

meth

minimum_edge_cut

meth

minimum_node_cut

meth

node_connectivity

meth

preflow_push

meth

shortest_augmenting_path

meth

stoer_wagner

meth

Examples

This function is not imported in the base NetworkX namespace, so you have to explicitly import it from the connectivity package:

>>> from networkx.algorithms.connectivity import minimum_st_edge_cut

We use in this example the platonic icosahedral graph, which has edge connectivity 5.

>>> G = nx.icosahedral_graph()
... len(minimum_st_edge_cut(G, 0, 6)) 5

If you need to compute local edge cuts on several pairs of nodes in the same graph, it is recommended that you reuse the data structures that NetworkX uses in the computation: the auxiliary digraph for edge connectivity, and the residual network for the underlying maximum flow computation.

Example of how to compute local edge cuts among all pairs of nodes of the platonic icosahedral graph reusing the data structures.

>>> import itertools
... # You also have to explicitly import the function for
... # building the auxiliary digraph from the connectivity package
... from networkx.algorithms.connectivity import build_auxiliary_edge_connectivity
... H = build_auxiliary_edge_connectivity(G)
... # And the function for building the residual network from the
... # flow package
... from networkx.algorithms.flow import build_residual_network
... # Note that the auxiliary digraph has an edge attribute named capacity
... R = build_residual_network(H, "capacity")
... result = dict.fromkeys(G, dict())
... # Reuse the auxiliary digraph and the residual network by passing them
... # as parameters
... for u, v in itertools.combinations(G, 2):
...  k = len(minimum_st_edge_cut(G, u, v, auxiliary=H, residual=R))
...  result[u][v] = k
... all(result[u][v] == 5 for u, v in itertools.combinations(G, 2)) True

You can also use alternative flow algorithms for computing edge cuts. For instance, 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(minimum_st_edge_cut(G, 0, 6, flow_func=shortest_augmenting_path)) 5
See :

Back References

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

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#24
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