# networkx.algorithms.tree.mst.minimum_spanning_tree¶

minimum_spanning_tree(G, weight='weight', algorithm='kruskal', ignore_nan=False)[source]

Returns a minimum spanning tree or forest on an undirected graph G.

Parameters
• G (undirected graph) – An undirected graph. If G is connected, then the algorithm finds a spanning tree. Otherwise, a spanning forest is found.

• weight (str) – Data key to use for edge weights.

• algorithm (string) – The algorithm to use when finding a minimum spanning tree. Valid choices are ‘kruskal’, ‘prim’, or ‘boruvka’. The default is ‘kruskal’.

• ignore_nan (bool (default: False)) – If a NaN is found as an edge weight normally an exception is raised. If ignore_nan is True then that edge is ignored instead.

Returns

G – A minimum spanning tree or forest.

Return type

NetworkX Graph

Examples

>>> G = nx.cycle_graph(4)
>>> T = nx.minimum_spanning_tree(G)
>>> sorted(T.edges(data=True))
[(0, 1, {}), (1, 2, {}), (2, 3, {})]


Notes

For Borůvka’s algorithm, each edge must have a weight attribute, and each edge weight must be distinct.

For the other algorithms, if the graph edges do not have a weight attribute a default weight of 1 will be used.

There may be more than one tree with the same minimum or maximum weight. See networkx.tree.recognition for more detailed definitions.

Isolated nodes with self-loops are in the tree as edgeless isolated nodes.