This documentation is for the development version 1.9.dev_20140421000007

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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: 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.

See also

all_shortest_paths, shortest_path


This algorithm uses a modified depth-first search to generate the paths [R249]. 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.


[R249](1, 2) R. Sedgewick, “Algorithms in C, Part 5: Graph Algorithms”, Addison Wesley Professional, 3rd ed., 2001.


>>> 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]]