scipy.sparse.csgraph.yen#
- scipy.sparse.csgraph.yen(csgraph, source, sink, K, *, directed=True, return_predecessors=False, unweighted=False)#
Yen’s K-Shortest Paths algorithm on a directed or undirected graph.
Added in version 1.14.0.
- Parameters:
- csgrapharray or sparse array, 2 dimensions
The N x N array of distances representing the input graph.
- sourceint
The index of the starting node for the paths.
- sinkint
The index of the ending node for the paths.
- Kint
The number of shortest paths to find.
- directedbool, optional
If
True
(default), then find the shortest path on a directed graph: only move from pointi
to pointj
along pathscsgraph[i, j]
. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j alongcsgraph[i, j]
orcsgraph[j, i]
.- return_predecessorsbool, optional
If
True
, return the size(M, N)
predecessor matrix. Default:False
.- 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. Default:False
.
- Returns:
- dist_arrayndarray
Array of size
M
of shortest distances between the source and sink nodes.dist_array[i]
gives the i-th shortest distance from the source to the sink along the graph.M
is the number of shortest paths found, which is less than or equal to K.- predecessorsndarray
Returned only if
return_predecessors == True
. The M x N matrix of predecessors, which can be used to reconstruct the shortest paths.M
is the number of shortest paths found, which is less than or equal to K. Rowi
of the predecessor matrix contains information on thei
-th shortest path from the source to the sink: each entrypredecessors[i, j]
gives the index of the previous node in the path from the source to nodej
. If the path does not pass via nodej
, thenpredecessors[i, j] = -9999
.
- Raises:
- NegativeCycleError:
If there are negative cycles in the graph
Notes
Yen’s algorithm is a graph search algorithm that finds single-source K-shortest loopless paths for a graph with nonnegative edge cost. The algorithm was published by Jin Y. Yen in 1971 and employs any shortest path algorithm to find the best path, then proceeds to find
K - 1
deviations of the best path.The algorithm is based on Dijsktra’s algorithm for finding each shortest path. In case there are negative edges in the graph, Johnson’s algorithm is applied.
If multiple valid solutions are possible, output may vary with SciPy and Python version.
References
Examples
>>> from scipy.sparse import csr_matrix >>> from scipy.sparse.csgraph import yen
>>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [2, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> graph = csr_matrix(graph) >>> print(graph) (np.int32(0), np.int32(1)) 1 (np.int32(0), np.int32(2)) 2 (np.int32(1), np.int32(3)) 1 (np.int32(2), np.int32(0)) 2 (np.int32(2), np.int32(3)) 3
>>> dist_array, predecessors = yen(csgraph=graph, source=0, sink=3, K=2, ... directed=False, return_predecessors=True) >>> dist_array array([2., 5.]) >>> predecessors array([[-9999, 0, -9999, 1], [-9999, -9999, 0, 2]], dtype=int32)