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). Where k 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 at source 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