floyd_warshall#

floyd_warshall(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:

distancedict: A dictionary, keyed by source and target, of shortest paths distances between nodes.

See also

floyd_warshall_predecessor_and_distance
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(
...     [(0, 1, 5), (1, 2, 2), (2, 3, -3), (1, 3, 10), (3, 2, 8)]
... )
>>> fw = nx.floyd_warshall(G, weight="weight")
>>> results = {a: dict(b) for a, b in fw.items()}
>>> print(results)
{0: {0: 0, 1: 5, 2: 7, 3: 4}, 1: {1: 0, 2: 2, 3: -1, 0: inf}, 2: {2: 0, 3: -3, 0: inf, 1: inf}, 3: {3: 0, 2: 8, 0: inf, 1: inf}}
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Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.