networkx.algorithms.shortest_paths.dense.floyd_warshall_numpy

floyd_warshall_numpy(G, nodelist=None, weight='weight')

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

Parameters

• G (NetworkX graph)

• nodelist (list, optional) – The rows and columns are ordered by the nodes in nodelist. If nodelist is None then the ordering is produced by G.nodes().

• weight (string, optional (default= ‘weight’)) – Edge data key corresponding to the edge weight.

Returns

distance – A matrix of shortest path distances between nodes. If there is no path between to nodes the corresponding matrix entry will be Inf.

Return type

NumPy matrix

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 \(O(n^2)\).