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scipy.sparse.csgraph.

# breadth_first_tree

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

  Return the tree generated by a breadth-first search

  Note that a breadth-first tree from a specified node is unique.

  Added in version 0.11.0.

  Parameters:
    csgraph array_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_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 breadth- 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          breadth first tree from (0)

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

  In compressed sparse representation, the solution looks like this:

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

  Note that the resulting graph is a Directed Acyclic Graph which spans the graph. A breadth-first tree from a given node is unique.