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diff --git a/lib/sqlalchemy/util/topological.py b/lib/sqlalchemy/util/topological.py
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+++ b/lib/sqlalchemy/util/topological.py
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+# util/topological.py
+# Copyright (C) 2005-2022 the SQLAlchemy authors and contributors
+# <see AUTHORS file>
+#
+# This module is part of SQLAlchemy and is released under
+# the MIT License: https://www.opensource.org/licenses/mit-license.php
+
+"""Topological sorting algorithms."""
+
+from .. import util
+from ..exc import CircularDependencyError
+
+__all__ = ["sort", "sort_as_subsets", "find_cycles"]
+
+
+def sort_as_subsets(tuples, allitems):
+
+    edges = util.defaultdict(set)
+    for parent, child in tuples:
+        edges[child].add(parent)
+
+    todo = list(allitems)
+    todo_set = set(allitems)
+
+    while todo_set:
+        output = []
+        for node in todo:
+            if todo_set.isdisjoint(edges[node]):
+                output.append(node)
+
+        if not output:
+            raise CircularDependencyError(
+                "Circular dependency detected.",
+                find_cycles(tuples, allitems),
+                _gen_edges(edges),
+            )
+
+        todo_set.difference_update(output)
+        todo = [t for t in todo if t in todo_set]
+        yield output
+
+
+def sort(tuples, allitems, deterministic_order=True):
+    """sort the given list of items by dependency.
+
+    'tuples' is a list of tuples representing a partial ordering.
+
+    deterministic_order is no longer used, the order is now always
+    deterministic given the order of "allitems".    the flag is there
+    for backwards compatibility with Alembic.
+
+    """
+
+    for set_ in sort_as_subsets(tuples, allitems):
+        for s in set_:
+            yield s
+
+
+def find_cycles(tuples, allitems):
+    # adapted from:
+    # https://neopythonic.blogspot.com/2009/01/detecting-cycles-in-directed-graph.html
+
+    edges = util.defaultdict(set)
+    for parent, child in tuples:
+        edges[parent].add(child)
+    nodes_to_test = set(edges)
+
+    output = set()
+
+    # we'd like to find all nodes that are
+    # involved in cycles, so we do the full
+    # pass through the whole thing for each
+    # node in the original list.
+
+    # we can go just through parent edge nodes.
+    # if a node is only a child and never a parent,
+    # by definition it can't be part of a cycle.  same
+    # if it's not in the edges at all.
+    for node in nodes_to_test:
+        stack = [node]
+        todo = nodes_to_test.difference(stack)
+        while stack:
+            top = stack[-1]
+            for node in edges[top]:
+                if node in stack:
+                    cyc = stack[stack.index(node) :]
+                    todo.difference_update(cyc)
+                    output.update(cyc)
+
+                if node in todo:
+                    stack.append(node)
+                    todo.remove(node)
+                    break
+            else:
+                node = stack.pop()
+    return output
+
+
+def _gen_edges(edges):
+    return set([(right, left) for left in edges for right in edges[left]])