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 allawed.

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:
  • NetworkXNoPath – If no path exists between source and target.
  • NetworkXError – If source or target nodes are not in the input graph.
  • NetworkXNotImplemented – If the input graph is a Multi[Di]Graph.

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.