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all_simple_paths(G, source, target, cutoff=None)

A simple path is a path with no repeated nodes.

Notes

This algorithm uses a modified depth-first search to generate the paths . 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 $n$.

This function does not check that a path exists between :None:None:`source` and :None:None:`target`. For large graphs, this may result in very long runtimes. Consider using has_path to check that a path exists between :None:None:`source` and :None:None:`target` before calling this function on large graphs.

Parameters

G : NetworkX graph
source : node: Starting node for path
target : nodes: Single node or iterable of nodes at which to end 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.

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

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]]

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

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

>>> from itertools import chain
>>> from itertools import product
>>> from itertools import starmap
>>> from functools import partial
>>>
>>> chaini = chain.from_iterable
>>>
>>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)])
>>> roots = (v for v, d in G.in_degree() if d == 0)
>>> leaves = (v for v, d in G.out_degree() if d == 0)
>>> all_paths = partial(nx.all_simple_paths, G)
>>> list(chaini(starmap(all_paths, product(roots, leaves))))
[[0, 1, 2], [0, 3, 2]]

>>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)])
>>> roots = (v for v, d in G.in_degree() if d == 0)
>>> leaves = (v for v, d in G.out_degree() if d == 0)
>>> all_paths = []
>>> for root in roots:
...     for leaf in leaves:
...         paths = nx.all_simple_paths(G, root, leaf)
...         all_paths.extend(paths)
>>> all_paths
[[0, 1, 2], [0, 3, 2]]

>>> G = nx.DiGraph([(0, 1), (2, 1), (1, 3), (1, 4)])
>>> roots = (v for v, d in G.in_degree() if d == 0)
>>> leaves = [v for v, d in G.out_degree() if d == 0]
>>> all_paths = []
>>> for root in roots:
...     paths = nx.all_simple_paths(G, root, leaves)
...     all_paths.extend(paths)
>>> all_paths
[[0, 1, 3], [0, 1, 4], [2, 1, 3], [2, 1, 4]]

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.dag.dag_longest_path_length networkx.algorithms.dag.dag_longest_path networkx.algorithms.simple_paths.shortest_simple_paths networkx.algorithms.simple_paths.all_simple_edge_paths

Local connectivity graph

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