minimum_spanning_tree¶

minimum_spanning_tree(G, weight='weight')[source]¶

Return a minimum spanning tree or forest of an undirected weighted graph.

A minimum spanning tree is a subgraph of the graph (a tree) with the minimum sum of edge weights.

If the graph is not connected a spanning forest is constructed. A spanning forest is a union of the spanning trees for each connected component of the graph.

Parameters :

G : NetworkX Graph

weight : string

Edge data key to use for weight (default ‘weight’).

Returns :

G : NetworkX Graph

A minimum spanning tree or forest.

Notes

Uses Kruskal’s algorithm.

If the graph edges do not have a weight attribute a default weight of 1 will be used.

Examples

>>> G=nx.cycle_graph(4)
>>> G.add_edge(0,3,weight=2) # assign weight 2 to edge 0-3
>>> T=nx.minimum_spanning_tree(G)
>>> print(sorted(T.edges(data=True)))
[(0, 1, {}), (1, 2, {}), (2, 3, {})]