scipy.sparse.csgraph.

Return a breadth-first ordering starting with specified node.

Note that a breadth-first order is not unique, but the tree which it generates is unique.

Parameters:
csgrapharray_like or sparse matrix

The N x N compressed sparse graph. The input csgraph will be converted to csr format for the calculation.

i_startint

The index of starting node.

directedbool, optional

If True (default), then operate 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 (default), then return the predecessor array (see below).

Returns:
node_arrayndarray, one dimension

The breadth-first list of nodes, starting with specified node. The length of node_array is the number of nodes reachable from the specified node.

predecessorsndarray, one dimension

Returned only if return_predecessors is True. The length-N list of predecessors of each node in a breadth-first tree. If node i is in the tree, then its parent is given by predecessors[i]. If node i is not in the tree (and for the parent node) then predecessors[i] = -9999.

Notes

If multiple valid solutions are possible, output may vary with SciPy and Python version.

Examples

```>>> from scipy.sparse import csr_matrix
```
```>>> 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
```
```>>> breadth_first_order(graph,0)
(array([0, 1, 2, 3], dtype=int32), array([-9999,     0,     0,     1], dtype=int32))
```