all_simple_edge_paths#
- all_simple_edge_paths(G, source, target, cutoff=None)[source]#
Generate lists of edges for all simple paths in G from source to target.
A simple path is a path with no repeated nodes.
- Parameters:
- GNetworkX graph
- sourcenode
Starting node for path
- targetnodes
Single node or iterable of nodes at which to end path
- cutoffinteger, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
- Returns:
- path_generator: generator
A generator that produces lists of simple paths. If there are no paths between the source and target within the given cutoff the generator produces no output. For multigraphs, the list of edges have elements of the form
(u,v,k)
. Wherek
corresponds to the edge key.
See also
all_shortest_paths
,shortest_path
,all_simple_paths
Notes
This algorithm uses a modified depth-first search to generate the paths [1]. A single path can be found in \(O(V+E)\) time but the number of simple paths in a graph can be very large, e.g. \(O(n!)\) in the complete graph of order \(n\).
References
[1]R. Sedgewick, “Algorithms in C, Part 5: Graph Algorithms”, Addison Wesley Professional, 3rd ed., 2001.
Examples
Print the simple path edges of a Graph:
>>> g = nx.Graph([(1, 2), (2, 4), (1, 3), (3, 4)]) >>> for path in sorted(nx.all_simple_edge_paths(g, 1, 4)): ... print(path) [(1, 2), (2, 4)] [(1, 3), (3, 4)]
Print the simple path edges of a MultiGraph. Returned edges come with their associated keys:
>>> mg = nx.MultiGraph() >>> mg.add_edge(1, 2, key="k0") 'k0' >>> mg.add_edge(1, 2, key="k1") 'k1' >>> mg.add_edge(2, 3, key="k0") 'k0' >>> for path in sorted(nx.all_simple_edge_paths(mg, 1, 3)): ... print(path) [(1, 2, 'k0'), (2, 3, 'k0')] [(1, 2, 'k1'), (2, 3, 'k0')]
When
source
is one of the targets, the empty path starting and ending atsource
without traversing any edge is considered a valid simple edge path and is included in the results:>>> G = nx.Graph() >>> G.add_node(0) >>> paths = list(nx.all_simple_edge_paths(G, 0, 0)) >>> for path in paths: ... print(path) [] >>> len(paths) 1