diff --git a/bigframes/core/bigframe_node.py b/bigframes/core/bigframe_node.py
index 9054ab9ba0..c8985e2c93 100644
--- a/bigframes/core/bigframe_node.py
+++ b/bigframes/core/bigframe_node.py
@@ -20,17 +20,7 @@
 import functools
 import itertools
 import typing
-from typing import (
-    Callable,
-    Dict,
-    Generator,
-    Iterable,
-    Mapping,
-    Sequence,
-    Set,
-    Tuple,
-    Union,
-)
+from typing import Callable, Dict, Generator, Iterable, Mapping, Sequence, Tuple, Union
 
 from bigframes.core import expression, field, identifiers
 import bigframes.core.schema as schemata
@@ -309,33 +299,31 @@ def unique_nodes(
                 seen.add(item)
                 stack.extend(item.child_nodes)
 
-    def edges(
+    def iter_nodes_topo(
         self: BigFrameNode,
-    ) -> Generator[Tuple[BigFrameNode, BigFrameNode], None, None]:
-        for item in self.unique_nodes():
-            for child in item.child_nodes:
-                yield (item, child)
-
-    def iter_nodes_topo(self: BigFrameNode) -> Generator[BigFrameNode, None, None]:
-        """Returns nodes from bottom up."""
-        queue = collections.deque(
-            [node for node in self.unique_nodes() if not node.child_nodes]
-        )
-
+    ) -> Generator[Tuple[BigFrameNode, Sequence[BigFrameNode]], None, None]:
+        """Returns nodes in topological order, using Kahn's algorithm."""
         child_to_parents: Dict[
-            BigFrameNode, Set[BigFrameNode]
-        ] = collections.defaultdict(set)
-        for parent, child in self.edges():
-            child_to_parents[child].add(parent)
-
-        yielded = set()
+            BigFrameNode, list[BigFrameNode]
+        ] = collections.defaultdict(list)
+        out_degree: Dict[BigFrameNode, int] = collections.defaultdict(int)
+
+        queue: collections.deque["BigFrameNode"] = collections.deque()
+        for node in list(self.unique_nodes()):
+            num_children = len(node.child_nodes)
+            out_degree[node] = num_children
+            if num_children == 0:
+                queue.append(node)
+            for child in node.child_nodes:
+                child_to_parents[child].append(node)
 
         while queue:
             item = queue.popleft()
-            yield item
-            yielded.add(item)
-            for parent in child_to_parents[item]:
-                if set(parent.child_nodes).issubset(yielded):
+            parents = child_to_parents.get(item, [])
+            yield item, parents
+            for parent in parents:
+                out_degree[parent] -= 1
+                if out_degree[parent] == 0:
                     queue.append(parent)
 
     def top_down(
@@ -376,7 +364,7 @@ def bottom_up(
         Returns the transformed root node.
         """
         results: dict[BigFrameNode, BigFrameNode] = {}
-        for node in list(self.iter_nodes_topo()):
+        for node, _ in list(self.iter_nodes_topo()):
             # child nodes have already been transformed
             result = node.transform_children(lambda x: results[x])
             result = transform(result)
@@ -387,7 +375,7 @@ def bottom_up(
     def reduce_up(self, reduction: Callable[[BigFrameNode, Tuple[T, ...]], T]) -> T:
         """Apply a bottom-up reduction to the tree."""
         results: dict[BigFrameNode, T] = {}
-        for node in list(self.iter_nodes_topo()):
+        for node, _ in list(self.iter_nodes_topo()):
             # child nodes have already been transformed
             child_results = tuple(results[child] for child in node.child_nodes)
             result = reduction(node, child_results)
diff --git a/tests/unit/core/compile/sqlglot/test_compile_concat.py b/tests/unit/core/compile/sqlglot/test_compile_concat.py
index ec7e83a4b0..d223ad967c 100644
--- a/tests/unit/core/compile/sqlglot/test_compile_concat.py
+++ b/tests/unit/core/compile/sqlglot/test_compile_concat.py
@@ -24,7 +24,6 @@
 def test_compile_concat(
     scalars_types_pandas_df: pd.DataFrame, compiler_session: bigframes.Session, snapshot
 ):
-    # TODO: concat two same dataframes, which SQL does not get reused.
     # TODO: concat dataframes from a gbq table but trigger a windows compiler.
     df1 = bpd.DataFrame(scalars_types_pandas_df, session=compiler_session)
     df1 = df1[["rowindex", "int64_col", "string_col"]]