bellman_ford(csgraph, directed=True, indices=None, return_predecessors=False, unweighted=False)
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.
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.
The N x N array of distances representing the input graph.
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]
if specified, only compute the paths from the points at the given indices.
If True, return the size (N, N) predecesor matrix
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.
if there are negative cycles in the graph
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.
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
Compute the shortest path lengths using the Bellman-Ford algorithm.
>>> from scipy.sparse import csr_matrix
... 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_matrix(graph)
... print(graph) (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 3) 3
>>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True)
... dist_matrix array([0., 1., 2., 2.])
>>> predecessors array([-9999, 0, 0, 1], dtype=int32)See :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.sparse.csgraph._shortest_path.bellman_ford
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