networkx.algorithms.simple_paths.shortest_simple_paths

shortest_simple_paths(G, source, target, weight=None)[source]
Generate all simple paths in the graph G from source to target,

starting from shortest ones.

A simple path is a path with no repeated nodes.

If a weighted shortest path search is to be used, no negative weights are allowed.

Parameters
  • G (NetworkX graph)

  • source (node) – Starting node for path

  • target (node) – Ending node for path

  • weight (string) – Name of the edge attribute to be used as a weight. If None all edges are considered to have unit weight. Default value None.

Returns

path_generator – A generator that produces lists of simple paths, in order from shortest to longest.

Return type

generator

Raises

Examples

>>> G = nx.cycle_graph(7)
>>> paths = list(nx.shortest_simple_paths(G, 0, 3))
>>> print(paths)
[[0, 1, 2, 3], [0, 6, 5, 4, 3]]

You can use this function to efficiently compute the k shortest/best paths between two nodes.

>>> from itertools import islice
>>> def k_shortest_paths(G, source, target, k, weight=None):
...     return list(islice(nx.shortest_simple_paths(G, source, target, weight=weight), k))
>>> for path in k_shortest_paths(G, 0, 3, 2):
...     print(path)
[0, 1, 2, 3]
[0, 6, 5, 4, 3]

Notes

This procedure is based on algorithm by Jin Y. Yen 1. Finding the first \(K\) paths requires \(O(KN^3)\) operations.

See also

all_shortest_paths(), shortest_path(), all_simple_paths()

References

1

Jin Y. Yen, “Finding the K Shortest Loopless Paths in a Network”, Management Science, Vol. 17, No. 11, Theory Series (Jul., 1971), pp. 712-716.