# networkx.algorithms.shortest_paths.dense.floyd_warshall¶

floyd_warshall(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

distance – A dictionary, keyed by source and target, of shortest paths distances between nodes.

Return type

dict

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 $$O(n^2)$$.