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
G (undirected Graph) – An undirected graph. If
G
is connected, then the algorithm finds a spanning tree. Otherwise, a spanning forest is found.algorithm (string) – The algorithm to use when finding a minimum spanning tree. Valid choices are ‘kruskal’, ‘prim’, or ‘boruvka’. The default is ‘kruskal’.
weight (string) – Edge data key to use for weight (default ‘weight’).
keys (bool) – Whether to yield edge key in multigraphs in addition to the edge. If
G
is not a multigraph, this is ignored.data (bool, optional) – If True yield the edge data along with the edge.
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
edges – An iterator over edges in a maximum spanning tree of
G
. Edges connecting nodesu
andv
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 keyk
will be reported in the third position in the edge tuple.data
indicates whether the edge datadictd
will appear at the end of the edge tuple.If
G
is not a multigraph, the tuples are(u, v, d)
ifdata
is True or(u, v)
ifdata
is False. Return type
iterator
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]]
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/