diff --git a/pytools/graph.py b/pytools/graph.py
index 5fb933af..a1f35761 100644
--- a/pytools/graph.py
+++ b/pytools/graph.py
@@ -83,6 +83,7 @@
     Mapping,
     MutableSet,
     Optional,
+    Protocol,
     Set,
     Tuple,
     TypeVar,
@@ -267,8 +268,13 @@ def __init__(self, node: NodeT) -> None:
         self.node = node
 
 
+class _SupportsLT(Protocol):
+    def __lt__(self, other: object) -> bool:
+        ...
+
+
 @dataclass(frozen=True)
-class HeapEntry(Generic[NodeT]):
+class _HeapEntry(Generic[NodeT]):
     """
     Helper class to compare associated keys while comparing the elements in
     heap operations.
@@ -277,9 +283,9 @@ class HeapEntry(Generic[NodeT]):
     <https://github.com/python/cpython/blob/8d21aa21f2cbc6d50aab3f420bb23be1d081dac4/Lib/heapq.py#L135-L138>.
     """
     node: NodeT
-    key: Any
+    key: _SupportsLT
 
-    def __lt__(self, other: HeapEntry) -> bool:
+    def __lt__(self, other: _HeapEntry[NodeT]) -> bool:
         return self.key < other.key
 
 
@@ -325,7 +331,7 @@ def compute_topological_order(graph: GraphT[NodeT],
     # heap: list of instances of HeapEntry(n) where 'n' is a node in
     # 'graph' with no predecessor. Nodes with no predecessors are the
     # schedulable candidates.
-    heap = [HeapEntry(n, keyfunc(n))
+    heap = [_HeapEntry(n, keyfunc(n))
             for n, num_preds in nodes_to_num_predecessors.items()
             if num_preds == 0]
     heapify(heap)
@@ -340,7 +346,7 @@ def compute_topological_order(graph: GraphT[NodeT],
         for child in graph.get(node_to_be_scheduled, ()):
             nodes_to_num_predecessors[child] -= 1
             if nodes_to_num_predecessors[child] == 0:
-                heappush(heap, HeapEntry(child, keyfunc(child)))
+                heappush(heap, _HeapEntry(child, keyfunc(child)))
 
     if len(order) != total_num_nodes:
         # any node which has a predecessor left is a part of a cycle
@@ -461,11 +467,11 @@ def as_graphviz_dot(graph: GraphT[NodeT],
     from pytools.graphviz import dot_escape
 
     if node_labels is None:
-        def node_labels(x):
+        def node_labels(x: NodeT) -> str:
             return str(x)
 
     if edge_labels is None:
-        def edge_labels(x, y):
+        def edge_labels(x: NodeT, y: NodeT) -> str:
             return ""
 
     node_to_id = {}
diff --git a/run-mypy.sh b/run-mypy.sh
index 244d6cc4..0220058b 100755
--- a/run-mypy.sh
+++ b/run-mypy.sh
@@ -6,5 +6,6 @@ mypy --show-error-codes pytools
 
 mypy --strict --follow-imports=silent \
     pytools/tag.py \
+    pytools/graph.py \
     pytools/datatable.py \
     pytools/persistent_dict.py