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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].
        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].
    connection : str, optional
        ['weak'|'strong'].  For directed graphs, the type of connection to
        use.  Nodes i and j are strongly connected if a path exists both
        from i to j and from j to i.  Nodes i and j are weakly connected if
        only one of these paths exists.  If directed == False, this keyword
        is not referenced.
    return_labels : bool, optional
        If True (default), then return the labels for each of the connected
        components.

    Returns
    -------
    n_components: int
        The number of connected components.
    labels: ndarray
        The length-N array of labels of the connected components.

    References
    ----------
    .. [1] D. J. Pearce, "An Improved Algorithm for Finding the Strongly
           Connected Components of a Directed Graph", Technical Report, 2005

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import connected_components

    >>> graph = [
    ... [ 0, 1 , 1, 0 , 0 ],
    ... [ 0, 0 , 1 , 0 ,0 ],
    ... [ 0, 0, 0, 0, 0],
    ... [0, 0 , 0, 0, 1],
    ... [0, 0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	1
      (1, 2)	1
      (3, 4)	1

    >>> n_components, labels = connected_components(csgraph=graph, directed=False, return_labels=True)
    >>> n_components
    2
    >>> labels
    array([0, 0, 0, 1, 1], dtype=int32)

    
    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.

    .. 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 breadth-
        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          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_matrix
    >>> from scipy.sparse.csgraph import breadth_first_tree
    >>> X = csr_matrix([[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.
    
    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.

    .. 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 breadth-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 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.

    Examples
    --------
    >>> 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)
      (0, 1)    1
      (0, 2)    2
      (1, 3)    1
      (2, 0)    2
      (2, 3)    3

    >>> breadth_first_order(graph,0)
    (array([0, 1, 2, 3], dtype=int32), array([-9999,     0,     0,     1], dtype=int32))

    
Routines for traversing graphs in compressed sparse format
connected_components (line 22)breadth_first_order (line 267)scipy.sparse.csgraph._toolsndarray is not C contiguousbreadth_first_tree (line 123)depth_first_order (line 449)depth_first_tree (line 193)connected_componentsreturn_predecessorscline_in_tracebackbreadth_first_treereconstruct_pathdepth_first_treevalidate_graphisspmatrix_csrisspmatrix_csc_traversal.pyxreturn_labelsscipy.sparsepredecessorsn_componentsdense_outputRuntimeErrorImportErrorisspmatrixcsr_matrixconnectionValueErrornode_listcsgraph_Tdirectedindicesi_startfloat64csgraphstronglabelsindptr__import__zerostocsrshaperangenumpylowerint32emptydtypeITYPEDTYPEweak__test____name____main__fillnpTBuffer dtype mismatch, expected %s%s%s but got %sBuffer dtype mismatch, expected '%s' but got %s in '%s.%s'%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject%s.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObjectDoes not understand character buffer dtype format string ('%c')Cannot convert %.200s to %.200sscipy/sparse/csgraph/_traversal.c%s() got multiple values for keyword argument '%U'%.200s() keywords must be strings%s() got an unexpected keyword argument '%U'__int__ returned non-int (type %.200s).  The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.__%.4s__ returned non-%.4s (type %.200s)value too large to convert to unsigned intcan't convert negative value to unsigned intUnexpected format string character: '%c'Expected a dimension of size %zu, got %zuExpected %d dimensions, got %dPython does not define a standard format string size for long double ('g')..Buffer dtype mismatch; next field is at offset %zd but %zd expectedBig-endian buffer not supported on little-endian compilerBuffer acquisition: Expected '{' after 'T'Cannot handle repeated arrays in format stringExpected a dimension of size %zu, got %dExpected a comma in format string, got '%c'Expected %d dimension(s), got %dUnexpected end of format string, expected ')'Buffer has wrong number of dimensions (expected %d, got %d)Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s)scipy.sparse.csgraph._traversal._breadth_first_undirectedOut of bounds on buffer access (axis %d)scipy.sparse.csgraph._traversal._breadth_first_directedscipy.sparse.csgraph._traversal._depth_first_undirectedscipy.sparse.csgraph._traversal._depth_first_directedtoo many values to unpack (expected %zd)value too large to convert to intscipy.sparse.csgraph._traversal._connected_components_undirectedBuffer acquisition failed on assignment; and then reacquiring the old buffer failed too!scipy.sparse.csgraph._traversal._connected_components_directedcalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseExceptionscipy.sparse.csgraph._traversal.connected_components%.200s() takes %.8s %zd positional argument%.1s (%zd given)scipy.sparse.csgraph._traversal.breadth_first_orderneed more than %zd value%.1s to unpackscipy.sparse.csgraph._traversal.breadth_first_treescipy.sparse.csgraph._traversal.depth_first_orderscipy.sparse.csgraph._traversal.depth_first_treescipy.sparse.csgraph._traversalcompiletime version %s of module '%.100s' does not match runtime version %sinit scipy.sparse.csgraph._traversal
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    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))

    
    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.

    .. 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 breadth-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 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.

    Examples
    --------
    >>> 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)
      (0, 1)    1
      (0, 2)    2
      (1, 3)    1
      (2, 0)    2
      (2, 3)    3

    >>> breadth_first_order(graph,0)
    (array([0, 1, 2, 3], dtype=int32), array([-9999,     0,     0,     1], dtype=int32))

    
    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.
    
    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.

    .. 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 breadth-
        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          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_matrix
    >>> from scipy.sparse.csgraph import breadth_first_tree
    >>> X = csr_matrix([[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.
    
    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].
        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].
    connection : str, optional
        ['weak'|'strong'].  For directed graphs, the type of connection to
        use.  Nodes i and j are strongly connected if a path exists both
        from i to j and from j to i.  Nodes i and j are weakly connected if
        only one of these paths exists.  If directed == False, this keyword
        is not referenced.
    return_labels : bool, optional
        If True (default), then return the labels for each of the connected
        components.

    Returns
    -------
    n_components: int
        The number of connected components.
    labels: ndarray
        The length-N array of labels of the connected components.

    References
    ----------
    .. [1] D. J. Pearce, "An Improved Algorithm for Finding the Strongly
           Connected Components of a Directed Graph", Technical Report, 2005

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import connected_components

    >>> graph = [
    ... [ 0, 1 , 1, 0 , 0 ],
    ... [ 0, 0 , 1 , 0 ,0 ],
    ... [ 0, 0, 0, 0, 0],
    ... [0, 0 , 0, 0, 1],
    ... [0, 0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	1
      (1, 2)	1
      (3, 4)	1

    >>> n_components, labels = connected_components(csgraph=graph, directed=False, return_labels=True)
    >>> n_components
    2
    >>> labels
    array([0, 0, 0, 1, 1], dtype=int32)

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