`scipy.sparse.csgraph._shortest_path:bellman_ford`

Signature

   def     bellman_ford (    csgraph    ,    directed    =  True   ,    indices    =  None   ,    return_predecessors    =  False   ,    unweighted    =  False     )

Summary

Compute the shortest path lengths using the Bellman-Ford algorithm.

Extended Summary

The Bellman-Ford algorithm can robustly deal with graphs with negative weights. If a negative cycle is detected, an error is raised. For graphs without negative edge weights, Dijkstra's algorithm may be faster.

Parameters

csgraph : array_like, or sparse array or 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]
indices : array_like or int, optional: if specified, only compute the paths from the points at the given indices.
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.

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, shape (n_indices, n_nodes,): Returned only if return_predecessors=True. If indices is None then n_indices = n_nodes and the shape of the matrix becomes (n_nodes, n_nodes). The 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

This routine is specially designed for graphs with negative edge weights. If all edge weights are positive, then Dijkstra's algorithm is a better choice.

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

Examples

from scipy.sparse import csr_array
from scipy.sparse.csgraph import bellman_ford

✓

graph = [
[0, 1 ,2, 0],
[0, 0, 0, 1],
[2, 0, 0, 3],
[0, 0, 0, 0]
]
graph = csr_array(graph)

✓

print(graph)

✗

dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True)
dist_matrix
predecessors

✓

Aliases

scipy.sparse.csgraph.bellman_ford