floyd_warshall

floyd_warshall(G, weight='weight')

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

Parameters:

GNetworkX graph

weightstring or function (default= ‘weight’)

If this is a string, then edge weights will be accessed via the edge attribute with this key (that is, the weight of the edge joining u to v will be G.edges[u, v][weight]). If no such edge attribute exists, the weight of the edge is assumed to be one.

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 or None to indicate a hidden edge.

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

>>> from pprint import pprint
>>> 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()}
>>> pprint(results)
{0: {0: 0, 1: 5, 2: 7, 3: 4},
 1: {0: inf, 1: 0, 2: 2, 3: -1},
 2: {0: inf, 1: inf, 2: 0, 3: -3},
 3: {0: inf, 1: inf, 2: 8, 3: 0}}
----

Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.