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.

Added in version 0.11.0.

Parameters:

csgrapharray_like or sparse array or 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.

Notes

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

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_array
>>> from scipy.sparse.csgraph import depth_first_tree
>>> X = csr_array([[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.