We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Join operation in trees---not handling label_attribute
<!-- If you have a general question about NetworkX, please use the discussions tab to create a new discussion -->

<!--- Provide a general summary of the issue in the Title above -->
[https://github.com/networkx/networkx/blob/main/networkx/algorithms/tree/operations.py](https://github.com/networkx/networkx/blob/main/networkx/algorithms/tree/operations.py)
1. The resulting graph of join operation in trees isn't including the old labels of inputs.
2.  Not handling the cases where label_attribute is passed as an argument.

### Current Behavior
![Screenshot from 2023-03-11 17-03-33](https://user-images.githubusercontent.com/88175932/224483929-b1ebff93-2e5e-46a6-9c6e-11de1dc53ca1.png)

<!--- Tell us what happens instead of the expected behavior -->

### Expected Behavior

![image](https://user-images.githubusercontent.com/88175932/224484244-9e9653fe-2aa8-4f02-9bee-39942a2ab08f.png)


<!--- Tell us what should happen -->

### Steps to Reproduce
As shown above
<!--- Provide a minimal example that reproduces the bug -->

### Environment

<!--- Please provide details about your local environment -->

Python version: 3.10.6
NetworkX version: 3.0

### Additional context
[https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.tree.operations.join.html](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.tree.operations.join.html)

<!--- Add any other context about the problem here, screenshots, etc. -->
Improve test coverage for operations.py (join)
<!-- If you have a general question about NetworkX, please use the discussions tab to create a new discussion -->

<!--- Provide a general summary of the issue in the Title above -->

### Current Behavior
https://app.codecov.io/gh/networkx/networkx/blob/main/networkx/algorithms/tree/operations.py  the current test coverage is 92.8%. There are still some cases needed to be handled.
<!--- Tell us what happens instead of the expected behavior -->

### Expected Behavior

<!--- Tell us what should happen -->
https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.tree.operations.join.html
1. Test case to check label_attribute should be added 
2. In the documentation its written that the inputs must be tree. But this function works for graphs too. Could you tell me if its for  trees or graphs as well?
### Steps to Reproduce

<!--- Provide a minimal example that reproduces the bug -->

### Environment

<!--- Please provide details about your local environment -->

Python version:3.10.6
NetworkX version:3.0

### Additional context

<!--- Add any other context about the problem here, screenshots, etc. -->


--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `networkx/algorithms/tree/operations.py`
Content:
```
1 """Operations on trees."""
2 from functools import partial
3 from itertools import accumulate, chain
4 
5 import networkx as nx
6 
7 __all__ = ["join"]
8 
9 
10 def join(rooted_trees, label_attribute=None):
11     """Returns a new rooted tree with a root node joined with the roots
12     of each of the given rooted trees.
13 
14     Parameters
15     ----------
16     rooted_trees : list
17         A list of pairs in which each left element is a NetworkX graph
18         object representing a tree and each right element is the root
19         node of that tree. The nodes of these trees will be relabeled to
20         integers.
21 
22     label_attribute : str
23         If provided, the old node labels will be stored in the new tree
24         under this node attribute. If not provided, the node attribute
25         ``'_old'`` will store the original label of the node in the
26         rooted trees given in the input.
27 
28     Returns
29     -------
30     NetworkX graph
31         The rooted tree whose subtrees are the given rooted trees. The
32         new root node is labeled 0. Each non-root node has an attribute,
33         as described under the keyword argument ``label_attribute``,
34         that indicates the label of the original node in the input tree.
35 
36     Notes
37     -----
38     Graph, edge, and node attributes are propagated from the given
39     rooted trees to the created tree. If there are any overlapping graph
40     attributes, those from later trees will overwrite those from earlier
41     trees in the tuple of positional arguments.
42 
43     Examples
44     --------
45     Join two full balanced binary trees of height *h* to get a full
46     balanced binary tree of depth *h* + 1::
47 
48         >>> h = 4
49         >>> left = nx.balanced_tree(2, h)
50         >>> right = nx.balanced_tree(2, h)
51         >>> joined_tree = nx.join([(left, 0), (right, 0)])
52         >>> nx.is_isomorphic(joined_tree, nx.balanced_tree(2, h + 1))
53         True
54 
55     """
56     if len(rooted_trees) == 0:
57         return nx.empty_graph(1)
58 
59     # Unzip the zipped list of (tree, root) pairs.
60     trees, roots = zip(*rooted_trees)
61 
62     # The join of the trees has the same type as the type of the first
63     # tree.
64     R = type(trees[0])()
65 
66     # Relabel the nodes so that their union is the integers starting at 1.
67     if label_attribute is None:
68         label_attribute = "_old"
69     relabel = partial(
70         nx.convert_node_labels_to_integers, label_attribute=label_attribute
71     )
72     lengths = (len(tree) for tree in trees[:-1])
73     first_labels = chain([0], accumulate(lengths))
74     trees = [
75         relabel(tree, first_label=first_label + 1)
76         for tree, first_label in zip(trees, first_labels)
77     ]
78 
79     # Get the relabeled roots.
80     roots = [
81         next(v for v, d in tree.nodes(data=True) if d.get("_old") == root)
82         for tree, root in zip(trees, roots)
83     ]
84 
85     # Remove the old node labels.
86     for tree in trees:
87         for v in tree:
88             tree.nodes[v].pop("_old")
89 
90     # Add all sets of nodes and edges, with data.
91     nodes = (tree.nodes(data=True) for tree in trees)
92     edges = (tree.edges(data=True) for tree in trees)
93     R.add_nodes_from(chain.from_iterable(nodes))
94     R.add_edges_from(chain.from_iterable(edges))
95 
96     # Add graph attributes; later attributes take precedent over earlier
97     # attributes.
98     for tree in trees:
99         R.graph.update(tree.graph)
100 
101     # Finally, join the subtrees at the root. We know 0 is unused by the
102     # way we relabeled the subtrees.
103     R.add_node(0)
104     R.add_edges_from((0, root) for root in roots)
105 
106     return R
107
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/networkx/algorithms/tree/operations.py b/networkx/algorithms/tree/operations.py
--- a/networkx/algorithms/tree/operations.py
+++ b/networkx/algorithms/tree/operations.py
@@ -78,25 +78,13 @@
 
     # Get the relabeled roots.
     roots = [
-        next(v for v, d in tree.nodes(data=True) if d.get("_old") == root)
+        next(v for v, d in tree.nodes(data=True) if d.get(label_attribute) == root)
         for tree, root in zip(trees, roots)
     ]
 
-    # Remove the old node labels.
+    # Add all sets of nodes and edges, attributes
     for tree in trees:
-        for v in tree:
-            tree.nodes[v].pop("_old")
-
-    # Add all sets of nodes and edges, with data.
-    nodes = (tree.nodes(data=True) for tree in trees)
-    edges = (tree.edges(data=True) for tree in trees)
-    R.add_nodes_from(chain.from_iterable(nodes))
-    R.add_edges_from(chain.from_iterable(edges))
-
-    # Add graph attributes; later attributes take precedent over earlier
-    # attributes.
-    for tree in trees:
-        R.graph.update(tree.graph)
+        R.update(tree)
 
     # Finally, join the subtrees at the root. We know 0 is unused by the
     # way we relabeled the subtrees.

{"golden_diff": "diff --git a/networkx/algorithms/tree/operations.py b/networkx/algorithms/tree/operations.py\n--- a/networkx/algorithms/tree/operations.py\n+++ b/networkx/algorithms/tree/operations.py\n@@ -78,25 +78,13 @@\n \n     # Get the relabeled roots.\n     roots = [\n-        next(v for v, d in tree.nodes(data=True) if d.get(\"_old\") == root)\n+        next(v for v, d in tree.nodes(data=True) if d.get(label_attribute) == root)\n         for tree, root in zip(trees, roots)\n     ]\n \n-    # Remove the old node labels.\n+    # Add all sets of nodes and edges, attributes\n     for tree in trees:\n-        for v in tree:\n-            tree.nodes[v].pop(\"_old\")\n-\n-    # Add all sets of nodes and edges, with data.\n-    nodes = (tree.nodes(data=True) for tree in trees)\n-    edges = (tree.edges(data=True) for tree in trees)\n-    R.add_nodes_from(chain.from_iterable(nodes))\n-    R.add_edges_from(chain.from_iterable(edges))\n-\n-    # Add graph attributes; later attributes take precedent over earlier\n-    # attributes.\n-    for tree in trees:\n-        R.graph.update(tree.graph)\n+        R.update(tree)\n \n     # Finally, join the subtrees at the root. We know 0 is unused by the\n     # way we relabeled the subtrees.\n", "issue": "Join operation in trees---not handling label_attribute\n<!-- If you have a general question about NetworkX, please use the discussions tab to create a new discussion -->\r\n\r\n<!--- Provide a general summary of the issue in the Title above -->\r\n[https://github.com/networkx/networkx/blob/main/networkx/algorithms/tree/operations.py](https://github.com/networkx/networkx/blob/main/networkx/algorithms/tree/operations.py)\r\n1. The resulting graph of join operation in trees isn't including the old labels of inputs.\r\n2.  Not handling the cases where label_attribute is passed as an argument.\r\n\r\n### Current Behavior\r\n![Screenshot from 2023-03-11 17-03-33](https://user-images.githubusercontent.com/88175932/224483929-b1ebff93-2e5e-46a6-9c6e-11de1dc53ca1.png)\r\n\r\n<!--- Tell us what happens instead of the expected behavior -->\r\n\r\n### Expected Behavior\r\n\r\n![image](https://user-images.githubusercontent.com/88175932/224484244-9e9653fe-2aa8-4f02-9bee-39942a2ab08f.png)\r\n\r\n\r\n<!--- Tell us what should happen -->\r\n\r\n### Steps to Reproduce\r\nAs shown above\r\n<!--- Provide a minimal example that reproduces the bug -->\r\n\r\n### Environment\r\n\r\n<!--- Please provide details about your local environment -->\r\n\r\nPython version: 3.10.6\r\nNetworkX version: 3.0\r\n\r\n### Additional context\r\n[https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.tree.operations.join.html](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.tree.operations.join.html)\r\n\r\n<!--- Add any other context about the problem here, screenshots, etc. -->\nImprove test coverage for operations.py (join)\n<!-- If you have a general question about NetworkX, please use the discussions tab to create a new discussion -->\r\n\r\n<!--- Provide a general summary of the issue in the Title above -->\r\n\r\n### Current Behavior\r\nhttps://app.codecov.io/gh/networkx/networkx/blob/main/networkx/algorithms/tree/operations.py  the current test coverage is 92.8%. There are still some cases needed to be handled.\r\n<!--- Tell us what happens instead of the expected behavior -->\r\n\r\n### Expected Behavior\r\n\r\n<!--- Tell us what should happen -->\r\nhttps://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.tree.operations.join.html\r\n1. Test case to check label_attribute should be added \r\n2. In the documentation its written that the inputs must be tree. But this function works for graphs too. Could you tell me if its for  trees or graphs as well?\r\n### Steps to Reproduce\r\n\r\n<!--- Provide a minimal example that reproduces the bug -->\r\n\r\n### Environment\r\n\r\n<!--- Please provide details about your local environment -->\r\n\r\nPython version:3.10.6\r\nNetworkX version:3.0\r\n\r\n### Additional context\r\n\r\n<!--- Add any other context about the problem here, screenshots, etc. -->\r\n\n", "before_files": [{"content": "\"\"\"Operations on trees.\"\"\"\nfrom functools import partial\nfrom itertools import accumulate, chain\n\nimport networkx as nx\n\n__all__ = [\"join\"]\n\n\ndef join(rooted_trees, label_attribute=None):\n    \"\"\"Returns a new rooted tree with a root node joined with the roots\n    of each of the given rooted trees.\n\n    Parameters\n    ----------\n    rooted_trees : list\n        A list of pairs in which each left element is a NetworkX graph\n        object representing a tree and each right element is the root\n        node of that tree. The nodes of these trees will be relabeled to\n        integers.\n\n    label_attribute : str\n        If provided, the old node labels will be stored in the new tree\n        under this node attribute. If not provided, the node attribute\n        ``'_old'`` will store the original label of the node in the\n        rooted trees given in the input.\n\n    Returns\n    -------\n    NetworkX graph\n        The rooted tree whose subtrees are the given rooted trees. The\n        new root node is labeled 0. Each non-root node has an attribute,\n        as described under the keyword argument ``label_attribute``,\n        that indicates the label of the original node in the input tree.\n\n    Notes\n    -----\n    Graph, edge, and node attributes are propagated from the given\n    rooted trees to the created tree. If there are any overlapping graph\n    attributes, those from later trees will overwrite those from earlier\n    trees in the tuple of positional arguments.\n\n    Examples\n    --------\n    Join two full balanced binary trees of height *h* to get a full\n    balanced binary tree of depth *h* + 1::\n\n        >>> h = 4\n        >>> left = nx.balanced_tree(2, h)\n        >>> right = nx.balanced_tree(2, h)\n        >>> joined_tree = nx.join([(left, 0), (right, 0)])\n        >>> nx.is_isomorphic(joined_tree, nx.balanced_tree(2, h + 1))\n        True\n\n    \"\"\"\n    if len(rooted_trees) == 0:\n        return nx.empty_graph(1)\n\n    # Unzip the zipped list of (tree, root) pairs.\n    trees, roots = zip(*rooted_trees)\n\n    # The join of the trees has the same type as the type of the first\n    # tree.\n    R = type(trees[0])()\n\n    # Relabel the nodes so that their union is the integers starting at 1.\n    if label_attribute is None:\n        label_attribute = \"_old\"\n    relabel = partial(\n        nx.convert_node_labels_to_integers, label_attribute=label_attribute\n    )\n    lengths = (len(tree) for tree in trees[:-1])\n    first_labels = chain([0], accumulate(lengths))\n    trees = [\n        relabel(tree, first_label=first_label + 1)\n        for tree, first_label in zip(trees, first_labels)\n    ]\n\n    # Get the relabeled roots.\n    roots = [\n        next(v for v, d in tree.nodes(data=True) if d.get(\"_old\") == root)\n        for tree, root in zip(trees, roots)\n    ]\n\n    # Remove the old node labels.\n    for tree in trees:\n        for v in tree:\n            tree.nodes[v].pop(\"_old\")\n\n    # Add all sets of nodes and edges, with data.\n    nodes = (tree.nodes(data=True) for tree in trees)\n    edges = (tree.edges(data=True) for tree in trees)\n    R.add_nodes_from(chain.from_iterable(nodes))\n    R.add_edges_from(chain.from_iterable(edges))\n\n    # Add graph attributes; later attributes take precedent over earlier\n    # attributes.\n    for tree in trees:\n        R.graph.update(tree.graph)\n\n    # Finally, join the subtrees at the root. We know 0 is unused by the\n    # way we relabeled the subtrees.\n    R.add_node(0)\n    R.add_edges_from((0, root) for root in roots)\n\n    return R\n", "path": "networkx/algorithms/tree/operations.py"}], "after_files": [{"content": "\"\"\"Operations on trees.\"\"\"\nfrom functools import partial\nfrom itertools import accumulate, chain\n\nimport networkx as nx\n\n__all__ = [\"join\"]\n\n\ndef join(rooted_trees, label_attribute=None):\n    \"\"\"Returns a new rooted tree with a root node joined with the roots\n    of each of the given rooted trees.\n\n    Parameters\n    ----------\n    rooted_trees : list\n        A list of pairs in which each left element is a NetworkX graph\n        object representing a tree and each right element is the root\n        node of that tree. The nodes of these trees will be relabeled to\n        integers.\n\n    label_attribute : str\n        If provided, the old node labels will be stored in the new tree\n        under this node attribute. If not provided, the node attribute\n        ``'_old'`` will store the original label of the node in the\n        rooted trees given in the input.\n\n    Returns\n    -------\n    NetworkX graph\n        The rooted tree whose subtrees are the given rooted trees. The\n        new root node is labeled 0. Each non-root node has an attribute,\n        as described under the keyword argument ``label_attribute``,\n        that indicates the label of the original node in the input tree.\n\n    Notes\n    -----\n    Graph, edge, and node attributes are propagated from the given\n    rooted trees to the created tree. If there are any overlapping graph\n    attributes, those from later trees will overwrite those from earlier\n    trees in the tuple of positional arguments.\n\n    Examples\n    --------\n    Join two full balanced binary trees of height *h* to get a full\n    balanced binary tree of depth *h* + 1::\n\n        >>> h = 4\n        >>> left = nx.balanced_tree(2, h)\n        >>> right = nx.balanced_tree(2, h)\n        >>> joined_tree = nx.join([(left, 0), (right, 0)])\n        >>> nx.is_isomorphic(joined_tree, nx.balanced_tree(2, h + 1))\n        True\n\n    \"\"\"\n    if len(rooted_trees) == 0:\n        return nx.empty_graph(1)\n\n    # Unzip the zipped list of (tree, root) pairs.\n    trees, roots = zip(*rooted_trees)\n\n    # The join of the trees has the same type as the type of the first\n    # tree.\n    R = type(trees[0])()\n\n    # Relabel the nodes so that their union is the integers starting at 1.\n    if label_attribute is None:\n        label_attribute = \"_old\"\n    relabel = partial(\n        nx.convert_node_labels_to_integers, label_attribute=label_attribute\n    )\n    lengths = (len(tree) for tree in trees[:-1])\n    first_labels = chain([0], accumulate(lengths))\n    trees = [\n        relabel(tree, first_label=first_label + 1)\n        for tree, first_label in zip(trees, first_labels)\n    ]\n\n    # Get the relabeled roots.\n    roots = [\n        next(v for v, d in tree.nodes(data=True) if d.get(label_attribute) == root)\n        for tree, root in zip(trees, roots)\n    ]\n\n    # Add all sets of nodes and edges, attributes\n    for tree in trees:\n        R.update(tree)\n\n    # Finally, join the subtrees at the root. We know 0 is unused by the\n    # way we relabeled the subtrees.\n    R.add_node(0)\n    R.add_edges_from((0, root) for root in roots)\n\n    return R\n", "path": "networkx/algorithms/tree/operations.py"}]}