# Source code for networkx.algorithms.tree.operations

```
"""Operations on trees."""
from functools import partial
from itertools import accumulate, chain
import networkx as nx
__all__ = ["join_trees"]
# Argument types don't match dispatching, but allow manual selection of backend
[docs]
@nx._dispatchable(graphs=None, returns_graph=True)
def join_trees(rooted_trees, *, label_attribute=None, first_label=0):
"""Returns a new rooted tree made by joining `rooted_trees`
Constructs a new tree by joining each tree in `rooted_trees`.
A new root node is added and connected to each of the roots
of the input trees. While copying the nodes from the trees,
relabeling to integers occurs. If the `label_attribute` is provided,
the old node labels will be stored in the new tree under this attribute.
Parameters
----------
rooted_trees : list
A list of pairs in which each left element is a NetworkX graph
object representing a tree and each right element is the root
node of that tree. The nodes of these trees will be relabeled to
integers.
label_attribute : str
If provided, the old node labels will be stored in the new tree
under this node attribute. If not provided, the original labels
of the nodes in the input trees are not stored.
first_label : int, optional (default=0)
Specifies the label for the new root node. If provided, the root node of the joined tree
will have this label. If not provided, the root node will default to a label of 0.
Returns
-------
NetworkX graph
The rooted tree resulting from joining the provided `rooted_trees`. The new tree has a root node
labeled as specified by `first_label` (defaulting to 0 if not provided). Subtrees from the input
`rooted_trees` are attached to this new root node. Each non-root node, if the `label_attribute`
is provided, has an attribute that indicates the original label of the node in the input tree.
Notes
-----
Trees are stored in NetworkX as NetworkX Graphs. There is no specific
enforcement of the fact that these are trees. Testing for each tree
can be done using :func:`networkx.is_tree`.
Graph, edge, and node attributes are propagated from the given
rooted trees to the created tree. If there are any overlapping graph
attributes, those from later trees will overwrite those from earlier
trees in the tuple of positional arguments.
Examples
--------
Join two full balanced binary trees of height *h* to get a full
balanced binary tree of depth *h* + 1::
>>> h = 4
>>> left = nx.balanced_tree(2, h)
>>> right = nx.balanced_tree(2, h)
>>> joined_tree = nx.join_trees([(left, 0), (right, 0)])
>>> nx.is_isomorphic(joined_tree, nx.balanced_tree(2, h + 1))
True
"""
if not rooted_trees:
return nx.empty_graph(1)
# Unzip the zipped list of (tree, root) pairs.
trees, roots = zip(*rooted_trees)
# The join of the trees has the same type as the type of the first tree.
R = type(trees[0])()
lengths = (len(tree) for tree in trees[:-1])
first_labels = list(accumulate(lengths, initial=first_label + 1))
new_roots = []
for tree, root, first_node in zip(trees, roots, first_labels):
new_root = first_node + list(tree.nodes()).index(root)
new_roots.append(new_root)
# Relabel the nodes so that their union is the integers starting at first_label.
relabel = partial(
nx.convert_node_labels_to_integers, label_attribute=label_attribute
)
new_trees = [
relabel(tree, first_label=first_label)
for tree, first_label in zip(trees, first_labels)
]
# Add all sets of nodes and edges, attributes
for tree in new_trees:
R.update(tree)
# Finally, join the subtrees at the root. We know first_label is unused by the way we relabeled the subtrees.
R.add_node(first_label)
R.add_edges_from((first_label, root) for root in new_roots)
return R
```