shortest_path_length#

shortest_path_length(G, source=None, target=None, weight=None, method='dijkstra')[source]#

Compute shortest path lengths in the graph.

Parameters:

GNetworkX graph
sourcenode, optional: Starting node for path. If not specified, compute shortest path lengths using all nodes as source nodes.
targetnode, optional: Ending node for path. If not specified, compute shortest path lengths using all nodes as target 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 length. 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:

length: int or iterator

If the source and target are both specified, return the length of the shortest path from the source to the target.

If only the source is specified, return a dict keyed by target to the shortest path length from the source to that target.

If only the target is specified, return a dict keyed by source to the shortest path length from that source to the target.

If neither the source nor target are specified, return an iterator over (source, dictionary) where dictionary is keyed by target to shortest path length from source to that target.

Raises:

NodeNotFound: If source is not in G.
NetworkXNoPath: If no path exists between source and target.
ValueError: If method is not among the supported options.

See also

all_pairs_shortest_path_length
all_pairs_dijkstra_path_length
all_pairs_bellman_ford_path_length
single_source_shortest_path_length
single_source_dijkstra_path_length
single_source_bellman_ford_path_length

Notes

The length of the path is always 1 less than the number of nodes involved in the path since the length measures the number of edges followed.

For digraphs this returns the shortest directed path length. To find path lengths in the reverse direction use G.reverse(copy=False) first to flip the edge orientation.

Examples

>>> G = nx.path_graph(5)
>>> nx.shortest_path_length(G, source=0, target=4)
4
>>> p = nx.shortest_path_length(G, source=0)  # target not specified
>>> p[4]
4
>>> p = nx.shortest_path_length(G, target=4)  # source not specified
>>> p[0]
4
>>> p = dict(nx.shortest_path_length(G))  # source,target not specified
>>> p[0][4]
4