Note

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

# 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
• G (NetworkX graph)

• weight (string, optional (default= ‘weight’)) – Edge data key corresponding to the edge weight.

Returns

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

Return type

dictionaries

Examples

>>> G = nx.DiGraph()
...     [
...         ("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']


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 $$O(n^2)$$.

floyd_warshall(), floyd_warshall_numpy(), all_pairs_shortest_path(), all_pairs_shortest_path_length()