diff --git a/src/cyclebane/graph.py b/src/cyclebane/graph.py
index 682e9c6..1a6af40 100644
--- a/src/cyclebane/graph.py
+++ b/src/cyclebane/graph.py
@@ -430,7 +430,8 @@ def __setitem__(self, branch: Hashable | slice, other: Graph) -> None:
         intersection_nodes = set(graph.nodes) & set(new_branch.nodes) - {branch}
 
         for node in intersection_nodes:
-            if graph.pred[node] != new_branch.pred[node]:
+            new_pred = new_branch.pred[node]
+            if new_pred and graph.pred[node] != new_pred:
                 raise ValueError(
                     f"Node inputs differ for node '{node}':\n"
                     f"  {graph.pred[node]}\n"
diff --git a/tests/graph_test.py b/tests/graph_test.py
index d036679..c204666 100644
--- a/tests/graph_test.py
+++ b/tests/graph_test.py
@@ -639,6 +639,49 @@ def test_setitem_preserves_nodes_that_are_ancestors_of_unrelated_node() -> None:
     nx.utils.graphs_equal(graph.to_networkx(), g)
 
 
+def test_setitem_inserts_graph_with_missing_parent() -> None:
+    g1 = nx.DiGraph()
+    g1.add_edge('a', 'b')
+    g1.add_edge('n', 'c')
+    g2 = nx.DiGraph()
+    g2.add_edge('b', 'n')
+
+    graph = cb.Graph(g1)
+    graph['n'] = cb.Graph(g2)
+    expected = g1.copy()
+    expected.add_edge('b', 'n')
+    nx.utils.graphs_equal(graph.to_networkx(), expected)
+
+
+def test_setitem_fails_with_partial_parent_mismatch() -> None:
+    g1 = nx.DiGraph()
+    g1.add_edge('a', 'b')  # only in g1
+    g1.add_edge('e', 'b')  # in both graphs
+    g1.add_edge('n', 'c')
+    g2 = nx.DiGraph()
+    g2.add_edge('b', 'n')
+    g2.add_edge('e', 'b')  # in both graphs
+    g2.add_edge('x', 'b')  # only in g2
+
+    graph = cb.Graph(g1)
+    with pytest.raises(ValueError, match="Node inputs differ for node 'b'"):
+        graph['n'] = cb.Graph(g2)
+
+
+def test_setitem_fails_when_grandparents_change() -> None:
+    g1 = nx.DiGraph()
+    g1.add_edge('a1', 'b')
+    g1.add_edge('a2', 'b')
+    g1.add_edge('b', 'c')
+    g2 = nx.DiGraph()  # no a2 -> b edge
+    g2.add_edge('a1', 'b')
+    g2.add_edge('b', 'c')
+
+    graph = cb.Graph(g1)
+    with pytest.raises(ValueError, match="Node inputs differ for node 'b'"):
+        graph['c'] = cb.Graph(g2)
+
+
 def test_getitem_returns_graph_containing_only_key_and_ancestors() -> None:
     g = nx.DiGraph()
     g.add_edge('a', 'b')