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# 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 : | csgraph : array_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_start : int The index of starting node. directed : bool, 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 : | cstree : csr 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.

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