bundles / scipy 1.17.1 / scipy / sparse / csgraph / _shortest_path / shortest_path

cython_function_or_method

`scipy.sparse.csgraph._shortest_path:shortest_path`

Signature

   def     shortest_path (    csgraph    ,    method    =  auto   ,    directed    =  True   ,    return_predecessors    =  False   ,    unweighted    =  False   ,    overwrite    =  False   ,    indices    =  None     )

Summary

Perform a shortest-path graph search on a positive directed or undirected graph.

Extended Summary

Parameters

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

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

method : string ['auto'|'FW'|'D'], optional

Algorithm to use for shortest paths. Options are:

'auto' -- (default) select the best among 'FW', 'D', 'BF', or 'J'
based on the input data.
'FW' -- Floyd-Warshall algorithm.
Computational cost is approximately O[N^3]. The input csgraph will be converted to a dense representation.
'D' -- Dijkstra's algorithm with priority queue.
Computational cost is approximately O[I * (E + N) * log(N)], where E is the number of edges in the graph, and I = len(indices) if indices is passed. Otherwise, I = N. The input csgraph will be converted to a csr representation.
'BF' -- Bellman-Ford algorithm.
This algorithm can be used when weights are negative. If a negative cycle is encountered, an error will be raised. Computational cost is approximately O[N(N^2 k)], where k is the average number of connected edges per node. The input csgraph will be converted to a csr representation.
'J' -- Johnson's algorithm.
Like the Bellman-Ford algorithm, Johnson's algorithm is designed for use when the weights are negative. It combines the Bellman-Ford algorithm with Dijkstra's algorithm for faster computation.

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 method == 'FW' and csgraph is a dense, c-ordered array with dtype=float64.

indices : array_like or int, optional

If specified, only compute the paths from the points at the given indices. Incompatible with method == 'FW'.

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

As currently implemented, Dijkstra's algorithm and Johnson's algorithm do not work for graphs with direction-dependent distances when directed == False. i.e., if csgraph[i,j] and csgraph[j,i] are non-equal edges, method='D' may yield an incorrect result.

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 shortest_path

✓

graph = [
[0, 0, 7, 0],
[0, 0, 8, 5],
[7, 8, 0, 0],
[0, 5, 0, 0]
]
graph = csr_array(graph)

✓

print(graph)

✗

sources = [0, 2]
dist_matrix, predecessors = shortest_path(csgraph=graph, directed=False, indices=sources, return_predecessors=True)
dist_matrix
predecessors

✓

Reconstructing shortest paths from sources to all the nodes of the graph.

shortest_paths = {}
for idx in range(len(sources)):
    for node in range(4):
        curr_node = node # start from the destination node
        path = []
        while curr_node != -9999: # no previous node available, exit the loop
            path = [curr_node] + path # prefix the previous node obtained from the last iteration
            curr_node = int(predecessors[idx][curr_node]) # set current node to previous node
        shortest_paths[(sources[idx], node)] = path

✓

Computing the length of the shortest path from node 0 to node 3 of the graph. It can be observed that computed length and the ``dist_matrix`` value are exactly same.

shortest_paths[(0, 3)]
path03 = shortest_paths[(0, 3)]
sum([graph[path03[0], path03[1]], graph[path03[1], path03[2]], graph[path03[2], path03[3]]])
dist_matrix[0][3]

✓

Another example of computing shortest path length from node 2 to node 3. Here, ``dist_matrix[1][3]`` is used to get the length of the path returned by ``shortest_path``. This is because node 2 is the second source, so the lengths of the path from it to other nodes in the graph will be at index 1 in ``dist_matrix``.

shortest_paths[(2, 3)]
path23 = shortest_paths[(2, 3)]
sum([graph[path23[0], path23[1]], graph[path23[1], path23[2]]])
dist_matrix[1][3]

✓

Aliases

scipy.sparse.csgraph.shortest_path