floyd_warshall_predecessor_and_distance

floyd_warshall_predecessor_and_distance(G, weight='weight')

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']

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Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.