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 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 – 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.