diff --git a/src/docforge/manual_projection.py b/src/docforge/manual_projection.py
index 9e5640c..a249d38 100644
--- a/src/docforge/manual_projection.py
+++ b/src/docforge/manual_projection.py
@@ -24,47 +24,51 @@ def _cycles(node_ids: tuple[str, ...], edges: tuple[Edge, ...]) -> list[list[str
     """Return deterministic strongly connected components that represent cycles."""
 
     adjacency: dict[str, list[str]] = {node_id: [] for node_id in node_ids}
+    reverse_adjacency: dict[str, list[str]] = {node_id: [] for node_id in node_ids}
     for edge in edges:
         adjacency[edge.source_id].append(edge.target_id)
-    for targets in adjacency.values():
+        reverse_adjacency[edge.target_id].append(edge.source_id)
+    for targets in (*adjacency.values(), *reverse_adjacency.values()):
         targets.sort()
 
-    index = 0
-    indexes: dict[str, int] = {}
-    lowlinks: dict[str, int] = {}
-    stack: list[str] = []
-    on_stack: set[str] = set()
-    components: list[list[str]] = []
+    visited: set[str] = set()
+    finished: list[str] = []
+    for node_id in node_ids:
+        if node_id in visited:
+            continue
+        visited.add(node_id)
+        traversal: list[tuple[str, int]] = [(node_id, 0)]
+        while traversal:
+            current, position = traversal[-1]
+            targets = adjacency[current]
+            if position < len(targets):
+                target = targets[position]
+                traversal[-1] = (current, position + 1)
+                if target not in visited:
+                    visited.add(target)
+                    traversal.append((target, 0))
+                continue
+            finished.append(current)
+            traversal.pop()
 
-    def visit(node_id: str) -> None:
-        nonlocal index
-        indexes[node_id] = index
-        lowlinks[node_id] = index
-        index += 1
-        stack.append(node_id)
-        on_stack.add(node_id)
-        for target_id in adjacency[node_id]:
-            if target_id not in indexes:
-                visit(target_id)
-                lowlinks[node_id] = min(lowlinks[node_id], lowlinks[target_id])
-            elif target_id in on_stack:
-                lowlinks[node_id] = min(lowlinks[node_id], indexes[target_id])
-        if lowlinks[node_id] != indexes[node_id]:
-            return
+    assigned: set[str] = set()
+    components: list[list[str]] = []
+    for node_id in reversed(finished):
+        if node_id in assigned:
+            continue
+        assigned.add(node_id)
         component: list[str] = []
-        while stack:
-            member = stack.pop()
-            on_stack.remove(member)
-            component.append(member)
-            if member == node_id:
-                break
+        component_stack = [node_id]
+        while component_stack:
+            current = component_stack.pop()
+            component.append(current)
+            for target in reversed(reverse_adjacency[current]):
+                if target not in assigned:
+                    assigned.add(target)
+                    component_stack.append(target)
         component.sort()
         if len(component) > 1 or component[0] in adjacency[component[0]]:
             components.append(component)
-
-    for node_id in node_ids:
-        if node_id not in indexes:
-            visit(node_id)
     return sorted(components)
 
 
diff --git a/tests/test_projection_contract.py b/tests/test_projection_contract.py
index 26592ae..27844cb 100644
--- a/tests/test_projection_contract.py
+++ b/tests/test_projection_contract.py
@@ -14,6 +14,7 @@ from unittest import mock
 
 from docforge.errors import DocForgeError
 from docforge.manual_projection import (
+    _cycles,
     build_manual_projection_package,
     build_manual_render_plan,
 )
@@ -390,6 +391,21 @@ class ProjectionContractTests(unittest.TestCase):
             workflow["cross_references"],
         )
 
+    def test_cycle_detection_handles_the_maximum_deep_graph_iteratively(self) -> None:
+        node_ids = tuple(f"node.{index:05d}" for index in range(10_000))
+        chain = tuple(
+            Edge(node_ids[index], "depends_on", node_ids[index + 1])
+            for index in range(len(node_ids) - 1)
+        )
+        self.assertEqual([], _cycles(node_ids, chain))
+        self.assertEqual(
+            [list(node_ids)],
+            _cycles(
+                node_ids,
+                (*chain, Edge(node_ids[-1], "depends_on", node_ids[0])),
+            ),
+        )
+
     def test_alpha_compatibility_shim_preserves_legacy_identity_and_bytes(self) -> None:
         renderer = GenericHtmlRenderer()
         self.assertEqual(ALPHA_RENDERER_VERSION, renderer.renderer_version)