all_simple_paths¶

all_simple_paths(G, source, target, cutoff=None)[source]¶

Generate all simple paths in the graph G from source to target.

A simple path is a path with no repeated nodes.

Parameters:	G (NetworkX graph) – source (node) – Starting node for path target (node) – Ending node for path cutoff (integer, optional) – Depth to stop the search. Only paths of length <= cutoff are returned.
Returns:	path_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.
Return type:	generator

Examples

>>> G = nx.complete_graph(4)
>>> for path in nx.all_simple_paths(G, source=0, target=3):
...     print(path)
...
[0, 1, 2, 3]
[0, 1, 3]
[0, 2, 1, 3]
[0, 2, 3]
[0, 3]
>>> paths = nx.all_simple_paths(G, source=0, target=3, cutoff=2)
>>> print(list(paths))
[[0, 1, 3], [0, 2, 3], [0, 3]]

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.