diff --git a/src/daglib/dag.py b/src/daglib/dag.py
index 76efa9a..760774f 100644
--- a/src/daglib/dag.py
+++ b/src/daglib/dag.py
@@ -70,10 +70,10 @@ class DAG(Generic[T], MutableMapping[T, DAGSetView[T]]):
             if add_hook := getattr(self, "on_add", None):
                 add_hook(u, v)
 
-        def _on_remove(u: T) -> None:
-            self.__dagdel__(u)
+        def _on_remove(v: T) -> None:
+            self.__dagdel__(u, v)
             if remove_hook := getattr(self, "on_remove", None):
-                remove_hook(u, u)
+                remove_hook(u, v)
 
         dagset = DAGSetView(self._succ.get(u))
         dagset.on_add = _on_add
@@ -97,20 +97,11 @@ class DAG(Generic[T], MutableMapping[T, DAGSetView[T]]):
     def add_edge(self, u: T, v: T) -> None:
         if u == v:
             raise ValueError("Self-loops are not allowed in a DAG")
-
-        if u not in self._succ:
-            self._succ[u] = set()
-        if v not in self._pred:
-            self._pred[v] = set()
-
-        if v not in self._succ[u]:
-            self._succ[u].add(v)
-            self._pred[v].add(u)
+        self[u] += v
 
     def remove_edge(self, u: T, v: T, *, missing_ok: bool = True) -> None:
         if v in self._succ.get(u, ()):
-            self._succ[u].remove(v)
-            self._pred[v].discard(u)
+            self[u] -= v
         elif not missing_ok:
             raise KeyError((u, v))
 
diff --git a/tests/test_dag.py b/tests/test_dag.py
index a81f581..3e77ced 100644
--- a/tests/test_dag.py
+++ b/tests/test_dag.py
@@ -27,23 +27,29 @@ class TestDAGOps:
             g.add_edge("foo", "bar")
             assert "foo" in g._succ
             assert "bar" in g._succ["foo"]
+            assert "bar" in g._pred
             assert "foo" in g._pred["bar"]
+            assert set(g["foo"]) == {"bar"}
 
         def test_add_multiple_edges(self) -> None:
             g = DAG[str]()
             g.add_edge("foo", "bar")
             g.add_edge("foo", "baz")
             g.add_edge("bar", "baz")
+
+            assert "foo" in g._succ
+            assert "bar" in g._succ["foo"]
+            assert "baz" in g._succ["foo"]
+            assert set(g["foo"]) == {"bar", "baz"}
+
+            assert "bar" in g._succ
+            assert "baz" in g._succ["bar"]
+            assert set(g["bar"]) == {"baz"}
+
             assert "bar" in g["foo"]
             assert "baz" in g["foo"]
             assert "baz" in g["bar"]
 
-        def test_add_edge_creates_nodes(self) -> None:
-            g = DAG[str]()
-            g.add_edge("foo", "bar")
-            assert "foo" in g._succ
-            assert "bar" in g._pred
-
         def test_self_loop_raises_error(self) -> None:
             g = DAG[str]()
             with pytest.raises(ValueError, match="Self-loops are not allowed"):