floyd_warshall_numpy(G, nodelist=None, weight='weight')[source]#

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

This algorithm for finding shortest paths takes advantage of matrix representations of a graph and works well for dense graphs where all-pairs shortest path lengths are desired. The results are returned as a NumPy array, distance[i, j], where i and j are the indexes of two nodes in nodelist. The entry distance[i, j] is the distance along a shortest path from i to j. If no path exists the distance is Inf.

GNetworkX graph
nodelistlist, optional (default=G.nodes)

The rows and columns are ordered by the nodes in nodelist. If nodelist is None then the ordering is produced by G.nodes. Nodelist should include all nodes in G.

weight: string, optional (default=’weight’)

Edge data key corresponding to the edge weight.

distance2D numpy.ndarray

A numpy array of shortest path distances between nodes. If there is no path between two nodes the value is Inf.


If nodelist is not a list of the nodes in G.


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 \(O(n^2)\).


>>> G = nx.DiGraph()
>>> G.add_weighted_edges_from([(0, 1, 5), (1, 2, 2), (2, 3, -3), (1, 3, 10), (3, 2, 8)])
>>> nx.floyd_warshall_numpy(G)
array([[ 0.,  5.,  7.,  4.],
       [inf,  0.,  2., -1.],
       [inf, inf,  0., -3.],
       [inf, inf,  8.,  0.]])

Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.