scipy.sparse.csgraph.breadth_first_order(csgraph, i_start, directed=True, return_predecessors=True)#

Return a breadth-first ordering starting with specified node.

Note that a breadth-first order is not unique, but the tree which it generates is unique.

Added in version 0.11.0.

csgrapharray_like or sparse matrix

The N x N compressed sparse graph. The input csgraph will be converted to csr format for the calculation.


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].

return_predecessorsbool, optional

If True (default), then return the predecessor array (see below).

node_arrayndarray, one dimension

The breadth-first list of nodes, starting with specified node. The length of node_array is the number of nodes reachable from the specified node.

predecessorsndarray, one dimension

Returned only if return_predecessors is True. The length-N list of predecessors of each node in a breadth-first tree. If node i is in the tree, then its parent is given by predecessors[i]. If node i is not in the tree (and for the parent node) then predecessors[i] = -9999.


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


>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import breadth_first_order
>>> graph = [
... [0, 1, 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
  (np.int32(0), np.int32(1))        1
  (np.int32(0), np.int32(2))        2
  (np.int32(1), np.int32(3))        1
  (np.int32(2), np.int32(0))        2
  (np.int32(2), np.int32(3))        3
>>> breadth_first_order(graph,0)
(array([0, 1, 2, 3], dtype=int32), array([-9999,     0,     0,     1], dtype=int32))