diff --git a/changelog.d/9118.misc b/changelog.d/9118.misc
new file mode 100644
index 0000000000..346741d982
--- /dev/null
+++ b/changelog.d/9118.misc
@@ -0,0 +1 @@
+Improve efficiency of large state resolutions.
diff --git a/synapse/util/iterutils.py b/synapse/util/iterutils.py
index f7b4857a84..6ef2b008a4 100644
--- a/synapse/util/iterutils.py
+++ b/synapse/util/iterutils.py
@@ -92,7 +92,7 @@ def sorted_topologically(
         node = heapq.heappop(zero_degree)
         yield node
 
-        for edge in reverse_graph[node]:
+        for edge in reverse_graph.get(node, []):
             if edge in degree_map:
                 degree_map[edge] -= 1
                 if degree_map[edge] == 0:
diff --git a/tests/util/test_itertools.py b/tests/util/test_itertools.py
index 1184cea5a3..522c8061f9 100644
--- a/tests/util/test_itertools.py
+++ b/tests/util/test_itertools.py
@@ -56,6 +56,14 @@ class SortTopologically(TestCase):
         graph = {}  # type: Dict[int, List[int]]
         self.assertEqual(list(sorted_topologically([], graph)), [])
 
+    def test_handle_empty_graph(self):
+        "Test that a graph where a node doesn't have an entry is treated as empty"
+
+        graph = {}  # type: Dict[int, List[int]]
+
+        # For disconnected nodes the output is simply sorted.
+        self.assertEqual(list(sorted_topologically([1, 2], graph)), [1, 2])
+
     def test_disconnected(self):
         "Test that a graph with no edges work"