networkx.algorithms.tree.mst.minimum_spanning_edges

minimum_spanning_edges(G, algorithm='kruskal', weight='weight', keys=True, data=True, ignore_nan=False)[source]

Generate edges in a minimum spanning 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. A spanning forest is a union of the spanning trees for each connected component of the graph.

Parameters
Gundirected Graph

An undirected graph. If G is connected, then the algorithm finds a spanning tree. Otherwise, a spanning forest is found.

algorithmstring

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

weightstring

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

keysbool

Whether to yield edge key in multigraphs in addition to the edge. If G is not a multigraph, this is ignored.

databool, optional

If True yield the edge data along with the edge.

ignore_nanbool (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
edgesiterator

An iterator over edges in a maximum spanning tree of G. Edges connecting nodes u and v are represented as tuples: (u, v, k, d) or (u, v, k) or (u, v, d) or (u, v)

If G is a multigraph, keys indicates whether the edge key k will be reported in the third position in the edge tuple. data indicates whether the edge datadict d will appear at the end of the edge tuple.

If G is not a multigraph, the tuples are (u, v, d) if data is True or (u, v) if data is False.

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.

Modified code from David Eppstein, April 2006 http://www.ics.uci.edu/~eppstein/PADS/

Examples

>>> from networkx.algorithms import tree

Find minimum spanning edges by Kruskal’s algorithm

>>> G = nx.cycle_graph(4)
>>> G.add_edge(0, 3, weight=2)
>>> mst = tree.minimum_spanning_edges(G, algorithm="kruskal", data=False)
>>> edgelist = list(mst)
>>> sorted(sorted(e) for e in edgelist)
[[0, 1], [1, 2], [2, 3]]

Find minimum spanning edges by Prim’s algorithm

>>> G = nx.cycle_graph(4)
>>> G.add_edge(0, 3, weight=2)
>>> mst = tree.minimum_spanning_edges(G, algorithm="prim", data=False)
>>> edgelist = list(mst)
>>> sorted(sorted(e) for e in edgelist)
[[0, 1], [1, 2], [2, 3]]