maximum_spanning_edges¶
- maximum_spanning_edges(G, algorithm='kruskal', weight='weight', keys=True, data=True, ignore_nan=False)[source]¶
Generate edges in a maximum spanning forest of an undirected weighted graph.
A maximum spanning tree is a subgraph of the graph (a tree) with the maximum possible 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 maximum 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 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.
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 maximum spanning edges by Kruskal’s algorithm
>>> G = nx.cycle_graph(4) >>> G.add_edge(0, 3, weight=2) >>> mst = tree.maximum_spanning_edges(G, algorithm="kruskal", data=False) >>> edgelist = list(mst) >>> sorted(sorted(e) for e in edgelist) [[0, 1], [0, 3], [1, 2]]
Find maximum spanning edges by Prim’s algorithm
>>> G = nx.cycle_graph(4) >>> G.add_edge(0, 3, weight=2) # assign weight 2 to edge 0-3 >>> mst = tree.maximum_spanning_edges(G, algorithm="prim", data=False) >>> edgelist = list(mst) >>> sorted(sorted(e) for e in edgelist) [[0, 1], [0, 3], [2, 3]]