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 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 `(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. Row `i` of 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 - 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)
<Compressed Sparse Row sparse matrix 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)
```