stoer_wagner(G, weight='weight', heap=<class 'networkx.utils.heaps.BinaryHeap'>)[source]#

Returns the weighted minimum edge cut using the Stoer-Wagner algorithm.

Determine the minimum edge cut of a connected graph using the Stoer-Wagner algorithm. In weighted cases, all weights must be nonnegative.

The running time of the algorithm depends on the type of heaps used:

Type of heap

Running time

Binary heap

\(O(n (m + n) \log n)\)

Fibonacci heap

\(O(nm + n^2 \log n)\)

Pairing heap

\(O(2^{2 \sqrt{\log \log n}} nm + n^2 \log n)\)

GNetworkX graph

Edges of the graph are expected to have an attribute named by the weight parameter below. If this attribute is not present, the edge is considered to have unit weight.


Name of the weight attribute of the edges. If the attribute is not present, unit weight is assumed. Default value: ‘weight’.


Type of heap to be used in the algorithm. It should be a subclass of MinHeap or implement a compatible interface.

If a stock heap implementation is to be used, BinaryHeap is recommended over PairingHeap for Python implementations without optimized attribute accesses (e.g., CPython) despite a slower asymptotic running time. For Python implementations with optimized attribute accesses (e.g., PyPy), PairingHeap provides better performance. Default value: BinaryHeap.

cut_valueinteger or float

The sum of weights of edges in a minimum cut.

partitionpair of node lists

A partitioning of the nodes that defines a minimum cut.


If the graph is directed or a multigraph.


If the graph has less than two nodes, is not connected or has a negative-weighted edge.


>>> G = nx.Graph()
>>> G.add_edge("x", "a", weight=3)
>>> G.add_edge("x", "b", weight=1)
>>> G.add_edge("a", "c", weight=3)
>>> G.add_edge("b", "c", weight=5)
>>> G.add_edge("b", "d", weight=4)
>>> G.add_edge("d", "e", weight=2)
>>> G.add_edge("c", "y", weight=2)
>>> G.add_edge("e", "y", weight=3)
>>> cut_value, partition = nx.stoer_wagner(G)
>>> cut_value