shortest_path

shortest_path(G, source=None, target=None, weight=None, method='dijkstra')

Compute shortest paths in the graph.

Parameters:

GNetworkX graph

sourcenode, optional

Starting node for path. If not specified, compute shortest paths for each possible starting node.

targetnode, optional

Ending node for path. If not specified, compute shortest paths to all possible nodes.

weightNone, string or function, optional (default = None)

If None, every edge has weight/distance/cost 1. If a string, use this edge attribute as the edge weight. Any edge attribute not present defaults to 1. If this 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.

methodstring, optional (default = ‘dijkstra’)

The algorithm to use to compute the path. Supported options: ‘dijkstra’, ‘bellman-ford’. Other inputs produce a ValueError. If weight is None, unweighted graph methods are used, and this suggestion is ignored.

Returns:

path: list or dictionary

All returned paths include both the source and target in the path.

If the source and target are both specified, return a single list of nodes in a shortest path from the source to the target.

If only the source is specified, return a dictionary keyed by targets with a list of nodes in a shortest path from the source to one of the targets.

If only the target is specified, return a dictionary keyed by sources with a list of nodes in a shortest path from one of the sources to the target.

If neither the source nor target are specified return a dictionary of dictionaries with path[source][target]=[list of nodes in path].

Raises:

NodeNotFound

If source is not in G.

ValueError

If method is not among the supported options.

See also

all_pairs_shortest_path

all_pairs_dijkstra_path

all_pairs_bellman_ford_path

single_source_shortest_path

single_source_dijkstra_path

single_source_bellman_ford_path

Notes

There may be more than one shortest path between a source and target. This returns only one of them.

Examples

>>> G = nx.path_graph(5)
>>> print(nx.shortest_path(G, source=0, target=4))
[0, 1, 2, 3, 4]
>>> p = nx.shortest_path(G, source=0)  # target not specified
>>> p[3] # shortest path from source=0 to target=3
[0, 1, 2, 3]
>>> p = nx.shortest_path(G, target=4)  # source not specified
>>> p[1] # shortest path from source=1 to target=4
[1, 2, 3, 4]
>>> p = nx.shortest_path(G)  # source, target not specified
>>> p[2][4] # shortest path from source=2 to target=4
[2, 3, 4]