diff --git a/cirkit/templates/region_graph/graph.py b/cirkit/templates/region_graph/graph.py
index eac1370a..694d8757 100644
--- a/cirkit/templates/region_graph/graph.py
+++ b/cirkit/templates/region_graph/graph.py
@@ -4,7 +4,7 @@
 from collections import defaultdict
 from collections.abc import Iterable, Iterator
 from functools import cached_property
-from typing import TypeAlias, TypedDict, Union, cast, final
+from typing import TypeAlias, TypedDict, cast, final
 
 import numpy as np
 from numpy.typing import NDArray
@@ -12,7 +12,7 @@
 from cirkit.utils.algorithms import DiAcyclicGraph
 from cirkit.utils.scope import Scope
 
-RGNodeMetadata: TypeAlias = dict[str, Union[int, float, str, bool]]
+RGNodeMetadata: TypeAlias = dict[str, int | float | str | bool]
 
 
 class RegionDict(TypedDict):
@@ -67,14 +67,10 @@ def __repr__(self) -> str:
 class RegionNode(RegionGraphNode):
     """The region node in the region graph."""
 
-    ...
-
 
 class PartitionNode(RegionGraphNode):
     """The partition node in the region graph."""
 
-    ...
-
 
 # We mark RG as final to hint that RG algorithms should not be its subclasses but factories, so that
 # constructed RGs and loaded RGs are all of type RegionGraph.
@@ -95,16 +91,19 @@ def _check_structure(self):
                 for ptn in node_children:
                     if not isinstance(ptn, PartitionNode):
                         raise ValueError(
-                            f"Expected partition node as children of '{node}', but found '{ptn}'"
+                            f"Expected partition node as children of '{node}', "
+                            f"but found '{ptn}'"
                         )
                     if ptn.scope != node.scope:
                         raise ValueError(
-                            f"Expectet partition node with scope '{node.scope}', but found '{ptn.scope}"
+                            f"Expected partition node with scope '{node.scope}', "
+                            f"but found '{ptn.scope}"
                         )
                 continue
             if not isinstance(node, PartitionNode):
                 raise ValueError(
-                    f"Region graph nodes must be either partition nodes or region nodes, found '{type(node)}'"
+                    f"Region graph nodes must be either partition nodes or region nodes, "
+                    f"found '{type(node)}'"
                 )
             scopes = []
             for rgn in node_children:
@@ -217,14 +216,17 @@ def is_compatible(self, other: "RegionGraph", /, *, scope: Iterable[int] | None
             if partition1.scope & scope != partition2.scope & scope:
                 continue  # Only check partitions with the same scope.
 
-            if any(partition1.scope <= input.scope for input in partition2.inputs) or any(
-                partition2.scope <= input.scope for input in partition1.inputs
+            partition1_inputs = self.node_inputs(partition1)
+            partition2_inputs = self.node_inputs(partition2)
+
+            if any(partition1.scope <= input.scope for input in partition2_inputs) or any(
+                partition2.scope <= input.scope for input in partition1_inputs
             ):
                 continue  # Only check partitions not within another partition.
 
-            adj_mat = np.zeros((len(partition1.inputs), len(partition2.inputs)), dtype=np.bool_)
+            adj_mat = np.zeros((len(partition1_inputs), len(partition2_inputs)), dtype=np.bool_)
             for (i, region1), (j, region2) in itertools.product(
-                enumerate(partition1.inputs), enumerate(partition2.inputs)
+                enumerate(partition1_inputs), enumerate(partition2_inputs)
             ):
                 # I.e., if scopes intersect over the scope to test.
                 adj_mat[i, j] = bool(region1.scope & region2.scope & scope)