Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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
GNetworkX graph
sourcenode

Starting node for path

targetnode

Ending node for path

weightstring or function

If it is a string, it is the name of the edge attribute to be used as a weight.

If it is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number.

If None all edges are considered to have unit weight. Default value None.

Returns
path_generator: generator

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

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.

See also

all_shortest_paths
shortest_path
all_simple_paths

Notes

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

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.

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]