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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.
.. versionadded:: 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.
depth_first_order(csgraph, i_start, directed=True, return_predecessors=True)
Return a depth-first ordering starting with specified node.
Note that a depth-first order is not unique. Furthermore, for graphs
with cycles, the tree generated by a depth-first search is not
unique either.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array_like or sparse matrix
The N x N 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].
return_predecessors : bool, optional
If True (default), then return the predecesor array (see below).
Returns
-------
node_array : ndarray, one dimension
The depth-first list of nodes, starting with specified node. The
length of node_array is the number of nodes reachable from the
specified node.
predecessors : ndarray, one dimension
Returned only if return_predecessors is True.
The length-N list of predecessors of each node in a depth-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.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import depth_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)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> depth_first_order(graph,0)
(array([0, 1, 3, 2], dtype=int32), array([-9999, 0, 0, 1], dtype=int32))
connected_components(csgraph, directed=True, connection='weak',
return_labels=True)
Analyze the connected components of a sparse graph
.. versionadded:: 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.
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].
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