diff --git a/onnxscript/ir/_core.py b/onnxscript/ir/_core.py
index faffde7483..14d07cb9f4 100644
--- a/onnxscript/ir/_core.py
+++ b/onnxscript/ir/_core.py
@@ -30,6 +30,7 @@
     Hashable,
     Iterable,
     Iterator,
+    NamedTuple,
     OrderedDict,
     Sequence,
     SupportsInt,
@@ -1055,6 +1056,18 @@ def _quoted(string: str) -> str:
     return f'"{string}"'
 
 
+class Usage(NamedTuple):
+    """A usage of a value in a node.
+
+    Attributes:
+        node: The node that uses the value.
+        idx: The input index of the value in the node.
+    """
+
+    node: Node
+    idx: int
+
+
 class Node(_protocols.NodeProtocol, _display.PrettyPrintable):
     """IR Node.
 
@@ -1293,6 +1306,25 @@ def inputs(self, _: Any) -> None:
             "Directly mutating the input sequence is unsupported. Please use Node.replace_input_with() instead."
         )
 
+    def predecessors(self) -> Sequence[Node]:
+        """Return the predecessor nodes of the node, deduplicated, in a deterministic order."""
+        # Use the ordered nature of a dictionary to deduplicate the nodes
+        predecessors: dict[Node, None] = {}
+        for value in self.inputs:
+            if value is not None and (producer := value.producer()) is not None:
+                predecessors[producer] = None
+        return tuple(predecessors)
+
+    def successors(self) -> Sequence[Node]:
+        """Return the successor nodes of the node, deduplicated, in a deterministic order."""
+        # Use the ordered nature of a dictionary to deduplicate the nodes
+        successors: dict[Node, None] = {}
+        for value in self.outputs:
+            assert value is not None, "Bug: Output values are not expected to be None"
+            for usage in value.uses():
+                successors[usage.node] = None
+        return tuple(successors)
+
     def replace_input_with(self, index: int, value: Value | None) -> None:
         """Replace an input with a new value."""
         if index < 0 or index >= len(self.inputs):
@@ -1564,7 +1596,7 @@ def __init__(
         # Use a collection of (Node, int) to store uses. This is needed
         # because a single use can use the same value multiple times.
         # Use a dictionary to preserve insertion order so that the visiting order is deterministic
-        self._uses: dict[tuple[Node, int], None] = {}
+        self._uses: dict[Usage, None] = {}
         self.doc_string = doc_string
 
     def __repr__(self) -> str:
@@ -1595,31 +1627,39 @@ def producer(self) -> Node | None:
         """
         return self._producer
 
+    def consumers(self) -> Sequence[Node]:
+        """Return the nodes (deduplicated) that consume this value."""
+        return tuple({usage.node: None for usage in self._uses})
+
     def index(self) -> int | None:
         """The index of the output of the defining node."""
         return self._index
 
-    def uses(self) -> Collection[tuple[Node, int]]:
+    def uses(self) -> Collection[Usage]:
         """Return a set of uses of the value.
 
         The set contains tuples of ``(Node, index)`` where the index is the index of the input
         of the node. For example, if ``node.inputs[1] == value``, then the use is ``(node, 1)``.
         """
-        return self._uses.keys()
+        # Create a tuple for the collection so that iteration on will will not
+        # be affected when the usage changes during graph mutation.
+        # This adds a small overhead but is better a user experience than
+        # having users call tuple().
+        return tuple(self._uses)
 
     def _add_usage(self, use: Node, index: int) -> None:
         """Add a usage of this value.
 
         This is an internal method. It should only be called by the Node class.
         """
-        self._uses[(use, index)] = None
+        self._uses[Usage(use, index)] = None
 
     def _remove_usage(self, use: Node, index: int) -> None:
         """Remove a node from the uses of this value.
 
         This is an internal method. It should only be called by the Node class.
         """
-        self._uses.pop((use, index))
+        self._uses.pop(Usage(use, index))
 
     @property
     def name(self) -> str | None:
diff --git a/onnxscript/ir/_core_test.py b/onnxscript/ir/_core_test.py
index 8662a8c01b..9b6cc94f6f 100644
--- a/onnxscript/ir/_core_test.py
+++ b/onnxscript/ir/_core_test.py
@@ -717,6 +717,13 @@ def test_is_dynamic_on_empty_shape(self):
 
 
 class ValueTest(unittest.TestCase):
+    def setUp(self) -> None:
+        self.v0 = _core.Value(name="v0")
+        self.v1 = _core.Value(name="v1")
+        self.node = _core.Node(
+            "test", "TestOp", inputs=(self.v0, self.v1, self.v1), num_outputs=2
+        )
+
     def test_initialize(self):
         _ = _core.Value()
 
@@ -732,14 +739,30 @@ def test_meta(self):
         value.metadata_props["test"] = "any string"
         self.assertEqual(value.metadata_props["test"], "any string")
 
+    def test_producer(self):
+        self.assertEqual(self.v0.producer(), None)
+        self.assertEqual(self.v1.producer(), None)
+        self.assertEqual(self.node.outputs[0].producer(), self.node)
+        self.assertEqual(self.node.outputs[1].producer(), self.node)
+
+    def test_consumers(self):
+        self.assertEqual(self.v0.consumers(), (self.node,))
+        self.assertEqual(self.v1.consumers(), (self.node,))
+        self.assertEqual(self.node.outputs[0].consumers(), ())
+        self.assertEqual(self.node.outputs[1].consumers(), ())
+
     # TODO(justinchuby): Test all methods
 
 
 class NodeTest(unittest.TestCase):
     def setUp(self) -> None:
-        self.v0 = _core.Value()
-        self.v1 = _core.Value()
-        self.node = _core.Node("test", "TestOp", inputs=(self.v0, self.v1), num_outputs=3)
+        self.v0 = _core.Value(name="v0")
+        self.v1 = _core.Value(name="v1")
+        self.node = _core.Node(
+            "test", "TestOp", inputs=(self.v0, self.v1, self.v1), num_outputs=3
+        )
+        self.node_a = _core.Node("test", "TestOpA", inputs=[self.node.outputs[0]])
+        self.node_b = _core.Node("test", "TestOpB", inputs=self.node.outputs)
 
     def test_it_is_hashable(self):
         self.assertIsInstance(hash(self.node), int)
@@ -748,7 +771,7 @@ def test_it_is_hashable(self):
     def test_init_with_values(self):
         self.assertEqual(self.node.domain, "test")
         self.assertEqual(self.node.op_type, "TestOp")
-        self.assertEqual(self.node.inputs, (self.v0, self.v1))
+        self.assertEqual(self.node.inputs, (self.v0, self.v1, self.v1))
         self.assertEqual(len(self.node.outputs), 3)
         self.assertEqual(self.node.attributes, {})
 
@@ -807,6 +830,23 @@ def test_it_is_added_to_a_graph_if_specified(self):
         )
         self.assertIn(self.node, graph)
 
+    def test_predecessors(self):
+        self.assertEqual(self.node.predecessors(), ())
+        self.assertEqual(self.node_a.predecessors(), (self.node,))
+        self.assertEqual(self.node_b.predecessors(), (self.node,))
+
+    def test_predecessors_are_unique(self):
+        # node_b has three inputs from node, but only one predecessor
+        self.assertEqual(self.node_b.predecessors(), (self.node,))
+
+    def test_successors(self):
+        self.assertEqual(self.node.successors(), (self.node_a, self.node_b))
+        self.assertEqual(self.node_a.successors(), ())
+        self.assertEqual(self.node_b.successors(), ())
+
+    def test_successors_are_unique(self):
+        self.assertEqual(self.node.successors(), (self.node_a, self.node_b))
+
     # TODO(justinchuby): Test all methods