scipy.sparse.csgraph.shortest_path¶

scipy.sparse.csgraph.
shortest_path
(csgraph, method='auto', directed=True, return_predecessors=False, unweighted=False, overwrite=False, indices=None)¶ Perform a shortestpath graph search on a positive directed or undirected graph.
New in version 0.11.0.
 Parameters
 csgrapharray, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
 methodstring [‘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’ – FloydWarshall algorithm. Computational cost is
approximately
O[N^3]
. The input csgraph will be converted to a dense representation. ‘D’ – Dijkstra’s algorithm with Fibonacci heaps. Computational
cost is approximately
O[N(N*k + N*log(N))]
, wherek
is the average number of connected edges per node. The input csgraph will be converted to a csr representation. ‘BF’ – BellmanFord 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)]
, wherek
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 BellmanFord algorithm,
Johnson’s algorithm is designed for use when the weights are negative. It combines the BellmanFord algorithm with Dijkstra’s algorithm for faster computation.
 directedbool, 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_predecessorsbool, optional
If True, return the size (N, N) predecesor matrix
 unweightedbool, 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.
 overwritebool, optional
If True, overwrite csgraph with the result. This applies only if method == ‘FW’ and csgraph is a dense, cordered array with dtype=float64.
 indicesarray_like or int, optional
If specified, only compute the paths for the points at the given indices. Incompatible with method == ‘FW’.
 Returns
 dist_matrixndarray
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.
 predecessorsndarray
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
As currently implemented, Dijkstra’s algorithm and Johnson’s algorithm do not work for graphs with directiondependent distances when directed == False. i.e., if csgraph[i,j] and csgraph[j,i] are nonequal edges, method=’D’ may yield an incorrect result.
Examples
>>> from scipy.sparse import csr_matrix >>> from scipy.sparse.csgraph import shortest_path
>>> 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 = shortest_path(csgraph=graph, directed=False, indices=0, return_predecessors=True) >>> dist_matrix array([ 0., 1., 2., 2.]) >>> predecessors array([9999, 0, 0, 1], dtype=int32)