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_like, or sparse array or matrix, 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 point- ito point- jalong 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- (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 - Mof 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.- Mis 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.- Mis the number of shortest paths found, which is less than or equal to K. Row- iof the predecessor matrix contains information on the- i-th shortest path from the source to the sink: each entry- predecessors[i, j]gives the index of the previous node in the path from the source to node- j. If the path does not pass via node- j, then- predecessors[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 - 1deviations 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_array >>> 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_array(graph) >>> print(graph) <Compressed Sparse Row sparse array of dtype 'int64' with 5 stored elements and shape (4, 4)> Coords Values (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 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)