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.

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.