diff --git a/onnxscript/ir/_core.py b/onnxscript/ir/_core.py
index b408898f7..876e09033 100644
--- a/onnxscript/ir/_core.py
+++ b/onnxscript/ir/_core.py
@@ -1145,22 +1145,24 @@ def __init__(
         Args:
             domain: The domain of the operator. For onnx operators, this is an empty string.
             op_type: The name of the operator.
-            inputs: The input values. When an input is None, it is an empty input.
+            inputs: The input values. When an input is ``None``, it is an empty input.
             attributes: The attributes. RefAttr can be used only when the node is defined in a Function.
             overload: The overload name when the node is invoking a function.
             num_outputs: The number of outputs of the node. If not specified, the number is 1.
-            outputs: The output values. If None, the outputs are created during initialization.
-            version: The version of the operator. If None, the version is unspecified and will follow that of the graph.
-            graph: The graph that the node belongs to. If None, the node is not added to any graph.
-                A `Node` must belong to zero or one graph.
-            name: The name of the node. If None, the node is anonymous.
+            outputs: The output values. If ``None``, the outputs are created during initialization.
+            version: The version of the operator. If ``None``, the version is unspecified and will follow that of the graph.
+            graph: The graph that the node belongs to. If ``None``, the node is not added to any graph.
+                A `Node` must belong to zero or one graph. If a :class:`Function`, the underlying graph
+                of the function is assigned to the node.
+            name: The name of the node. If ``None``, the node is anonymous. The name may be
+                set by a :class:`Graph` if ``graph`` is specified.
             doc_string: The documentation string.
             metadata_props: The metadata properties.
 
         Raises:
-            TypeError: If the attributes are not Attr or RefAttr.
-            ValueError: If `num_outputs`, when not None, is not the same as the length of the outputs.
-            ValueError: If an output value is None, when outputs is specified.
+            TypeError: If the attributes are not :class:`Attr` or :class:`RefAttr`.
+            ValueError: If ``num_outputs``, when not ``None``, is not the same as the length of the outputs.
+            ValueError: If an output value is ``None``, when outputs is specified.
             ValueError: If an output value has a producer set already, when outputs is specified.
         """
         self._name = name
@@ -1187,7 +1189,11 @@ def __init__(
         self._version: int | None = version
         self._metadata: _metadata.MetadataStore | None = None
         self._metadata_props: dict[str, str] | None = metadata_props
-        self._graph: Graph | Function | None = graph
+        # _graph is set by graph.append
+        self._graph: Graph | None = None
+        # Add the node to the graph if graph is specified
+        if graph is not None:
+            graph.append(self)
         self.doc_string = doc_string
 
         # Add the node as a use of the inputs
@@ -1195,10 +1201,6 @@ def __init__(
             if input_value is not None:
                 input_value._add_usage(self, i)  # pylint: disable=protected-access
 
-        # Add the node to the graph if graph is specified
-        if self._graph is not None:
-            self._graph.append(self)
-
     def _create_outputs(
         self, num_outputs: int | None, outputs: Sequence[Value] | None
     ) -> tuple[Value, ...]:
@@ -1432,11 +1434,11 @@ def metadata_props(self) -> dict[str, str]:
         return self._metadata_props
 
     @property
-    def graph(self) -> Graph | Function | None:
+    def graph(self) -> Graph | None:
         return self._graph
 
     @graph.setter
-    def graph(self, value: Graph | Function | None) -> None:
+    def graph(self, value: Graph | None) -> None:
         self._graph = value
 
     def op_identifier(self) -> _protocols.OperatorIdentifier:
@@ -2178,7 +2180,7 @@ def sort(self) -> None:
         # Obtain all nodes from the graph and its subgraphs for sorting
         nodes = list(onnxscript.ir.traversal.RecursiveGraphIterator(self))
         # Store the sorted nodes of each subgraph
-        sorted_nodes_by_graph: dict[Graph | Function, list[Node]] = {
+        sorted_nodes_by_graph: dict[Graph, list[Node]] = {
             graph: [] for graph in {node.graph for node in nodes if node.graph is not None}
         }
         # TODO: Explain why we need to store direct predecessors and children and why
diff --git a/onnxscript/ir/passes/common/constant_manipulation.py b/onnxscript/ir/passes/common/constant_manipulation.py
index 226bdfafc..888053a8f 100644
--- a/onnxscript/ir/passes/common/constant_manipulation.py
+++ b/onnxscript/ir/passes/common/constant_manipulation.py
@@ -67,9 +67,9 @@ def call(self, model: ir.Model) -> ir.passes.PassResult:
                 type=ir.TensorType(tensor.dtype),
                 const_value=tensor,
             )
-            assert isinstance(node.graph, ir.Graph)
+            assert node.graph is not None
             node.graph.register_initializer(initializer)
-            # Replace the constant node with the initilizer
+            # Replace the constant node with the initializer
             ir.convenience.replace_all_uses_with(node.outputs[0], initializer)
             node.graph.remove(node, safe=True)
             count += 1