# scipy.sparse.csgraph.depth_first_tree¶

scipy.sparse.csgraph.depth_first_tree(csgraph, i_start, directed=True)

Return a tree generated by a depth-first search.

Note that a tree generated by a depth-first search is not unique: it depends on the order that the children of each node are searched.

New in version 0.11.0.

Parameters
csgrapharray_like or sparse matrix

The N x N matrix representing the 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].

Returns
cstreecsr matrix

The N x N directed compressed-sparse representation of the depth- first tree drawn from csgraph, starting at the specified node.

Examples

The following example shows the computation of a depth-first tree over a simple four-component graph, starting at node 0:

``` input graph           depth first tree from (0)

(0)                         (0)
/   \                           \
3     8                           8
/       \                           \
(3)---5---(1)               (3)       (1)
\       /                   \       /
6     2                     6     2
\   /                       \   /
(2)                         (2)
```

In compressed sparse representation, the solution looks like this:

```>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import depth_first_tree
>>> X = csr_matrix([[0, 8, 0, 3],
...                 [0, 0, 2, 5],
...                 [0, 0, 0, 6],
...                 [0, 0, 0, 0]])
>>> Tcsr = depth_first_tree(X, 0, directed=False)
>>> Tcsr.toarray().astype(int)
array([[0, 8, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 6],
[0, 0, 0, 0]])
```

Note that the resulting graph is a Directed Acyclic Graph which spans the graph. Unlike a breadth-first tree, a depth-first tree of a given graph is not unique if the graph contains cycles. If the above solution had begun with the edge connecting nodes 0 and 3, the result would have been different.