Returns a set of nodes of minimum cardinality that disconnects G.
If source and target nodes are provided, this function returns the set of nodes of minimum cardinality that, if removed, would destroy all paths among source and target in G. If not, it returns a set of nodes of minimum cardinality that disconnects G.
Parameters: | G : NetworkX graph s : node
t : node
flow_func : function
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Returns: | cutset : set
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See also
minimum_st_node_cut(), minimum_cut(), minimum_edge_cut(), stoer_wagner(), node_connectivity(), edge_connectivity(), maximum_flow(), edmonds_karp(), preflow_push(), shortest_augmenting_path()
Notes
This is a flow based implementation of minimum node cut. The algorithm is based in solving a number of maximum flow computations to determine the capacity of the minimum cut on an auxiliary directed network that corresponds to the minimum node cut of G. It handles both directed and undirected graphs. This implementation is based on algorithm 11 in [R219].
References
[R219] | (1, 2) Abdol-Hossein Esfahanian. Connectivity Algorithms. http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf |
Examples
>>> # Platonic icosahedral graph has node connectivity 5
>>> G = nx.icosahedral_graph()
>>> node_cut = nx.minimum_node_cut(G)
>>> len(node_cut)
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
>>> node_cut == nx.minimum_node_cut(G, flow_func=shortest_augmenting_path)
True
If you specify a pair of nodes (source and target) as parameters, this function returns a local st node cut.
>>> len(nx.minimum_node_cut(G, 3, 7))
5
If you need to perform several local st cuts 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 minimum_st_node_cut() for details.