networkx.algorithms.shortest_paths.dense.floyd_warshall_predecessor_and_distance

floyd_warshall_predecessor_and_distance(G, weight='weight')[source]

Find all-pairs shortest path lengths using Floyd’s algorithm.

Parameters
GNetworkX graph
weight: string, optional (default= ‘weight’)

Edge data key corresponding to the edge weight.

Returns
predecessor,distancedictionaries

Dictionaries, keyed by source and target, of predecessors and distances in the shortest path.

See also

floyd_warshall
floyd_warshall_numpy
all_pairs_shortest_path
all_pairs_shortest_path_length

Notes

Floyd’s algorithm is appropriate for finding shortest paths in dense graphs or graphs with negative weights when Dijkstra’s algorithm fails. This algorithm can still fail if there are negative cycles. It has running time \(O(n^3)\) with running space of \(O(n^2)\).

Examples

>>> G = nx.DiGraph()
>>> G.add_weighted_edges_from(
...     [
...         ("s", "u", 10),
...         ("s", "x", 5),
...         ("u", "v", 1),
...         ("u", "x", 2),
...         ("v", "y", 1),
...         ("x", "u", 3),
...         ("x", "v", 5),
...         ("x", "y", 2),
...         ("y", "s", 7),
...         ("y", "v", 6),
...     ]
... )
>>> predecessors, _ = nx.floyd_warshall_predecessor_and_distance(G)
>>> print(nx.reconstruct_path("s", "v", predecessors))
['s', 'x', 'u', 'v']