join_trees(rooted_trees, *, label_attribute=None, first_label=0)[source]#

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.


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.


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_labelint, 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.

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.


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 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.


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([(left, 0), (right, 0)])
>>> nx.is_isomorphic(joined_tree, nx.balanced_tree(2, h + 1))