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# scipy.sparse.csgraph.floyd_warshall

scipy.sparse.csgraph.floyd_warshall(csgraph, directed=True, return_predecessors=False, unweighted=False, overwrite=False)

  Compute the shortest path lengths using the Floyd-Warshall algorithm

  New in version 0.11.0.

  Parameters:
    csgraph array, matrix, or sparse matrix, 2 dimensions

      The N x N array of distances representing the input graph.

    directed bool, optional

      If True (default), then find the shortest path on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]

    return_predecessors bool, optional

      If True, return the size (N, N) predecessor matrix.

    unweighted bool, optional

      If True, then find unweighted distances. That is, rather than finding the path between each point such that the sum of weights is minimized, find the path such that the number of edges is minimized.

    overwrite bool, optional

      If True, overwrite csgraph with the result. This applies only if csgraph is a dense, c-ordered array with dtype=float64.

  Returns:
    dist_matrix ndarray

      The N x N matrix of distances between graph nodes. dist_matrix[i,j] gives the shortest distance from point i to point j along the graph.

    predecessors ndarray

      Returned only if return_predecessors == True. The N x N matrix of predecessors, which can be used to reconstruct the shortest paths. Row i of the predecessor matrix contains information on the shortest paths from point i: each entry predecessors[i, j] gives the index of the previous node in the path from point i to point j. If no path exists between point i and j, then predecessors[i, j] = -9999

  Raises:
    NegativeCycleError:

      if there are negative cycles in the graph

  Notes

  If multiple valid solutions are possible, output may vary with SciPy and Python version.

  Examples

      >>> from scipy.sparse import csr_matrix
      >>> from scipy.sparse.csgraph import floyd_warshall

      >>> graph = [
      ... [0, 1, 2, 0],
      ... [0, 0, 0, 1],
      ... [2, 0, 0, 3],
      ... [0, 0, 0, 0]
      ... ]
      >>> graph = csr_matrix(graph)
      >>> print(graph)
        (0, 1)    1
        (0, 2)    2
        (1, 3)    1
        (2, 0)    2
        (2, 3)    3

      >>> dist_matrix, predecessors = floyd_warshall(csgraph=graph, directed=False, return_predecessors=True)
      >>> dist_matrix
      array([[0., 1., 2., 2.],
             [1., 0., 3., 1.],
             [2., 3., 0., 3.],
             [2., 1., 3., 0.]])
      >>> predecessors
      array([[-9999,     0,     0,     1],
             [    1, -9999,     0,     1],
             [    2,     0, -9999,     2],
             [    1,     3,     3, -9999]], dtype=int32)