diff --git a/django/db/migrations/graph.py b/django/db/migrations/graph.py
index 08481869f4..8d23b36cb7 100644
--- a/django/db/migrations/graph.py
+++ b/django/db/migrations/graph.py
@@ -19,8 +19,9 @@ class MigrationGraph(object):
     replacing migration, and repoint any dependencies that pointed to the
     replaced migrations to point to the replacing one.
 
-    A node should be a tuple: (app_path, migration_name) - but the code
-    here doesn't really care.
+    A node should be a tuple: (app_path, migration_name). The tree special-cases
+    things within an app - namely, root nodes and leaf nodes ignore dependencies
+    to other apps.
     """
 
     def __init__(self):
@@ -59,6 +60,31 @@ class MigrationGraph(object):
             raise ValueError("Node %r not a valid node" % node)
         return self.dfs(node, lambda x: self.dependents.get(x, set()))
 
+    def root_nodes(self):
+        """
+        Returns all root nodes - that is, nodes with no dependencies inside
+        their app. These are the starting point for an app.
+        """
+        roots = set()
+        for node in self.nodes:
+            if not filter(lambda key: key[0] == node[0], self.dependencies.get(node, set())):
+                roots.add(node)
+        return roots
+
+    def leaf_nodes(self):
+        """
+        Returns all leaf nodes - that is, nodes with no dependents in their app.
+        These are the "most current" version of an app's schema.
+        Having more than one per app is technically an error, but one that
+        gets handled further up, in the interactive command - it's usually the
+        result of a VCS merge and needs some user input.
+        """
+        leaves = set()
+        for node in self.nodes:
+            if not filter(lambda key: key[0] == node[0], self.dependents.get(node, set())):
+                leaves.add(node)
+        return leaves
+
     def dfs(self, start, get_children):
         """
         Dynamic programming based depth first search, for finding dependencies.
diff --git a/tests/migrations/tests.py b/tests/migrations/tests.py
index 56f4c9fdb9..338e28aa56 100644
--- a/tests/migrations/tests.py
+++ b/tests/migrations/tests.py
@@ -44,6 +44,15 @@ class GraphTests(TransactionTestCase):
             graph.backwards_plan(("app_b", "0002")),
             [('app_a', '0004'), ('app_a', '0003'), ('app_b', '0002')],
         )
+        # Test roots and leaves
+        self.assertEqual(
+            graph.root_nodes(),
+            set([('app_a', '0001'), ('app_b', '0001')]),
+        )
+        self.assertEqual(
+            graph.leaf_nodes(),
+            set([('app_a', '0004'), ('app_b', '0002')]),
+        )
 
     def test_complex_graph(self):
         """
@@ -81,6 +90,15 @@ class GraphTests(TransactionTestCase):
             graph.backwards_plan(("app_b", "0001")),
             [('app_a', '0004'), ('app_c', '0002'), ('app_c', '0001'), ('app_a', '0003'), ('app_b', '0002'), ('app_b', '0001')],
         )
+        # Test roots and leaves
+        self.assertEqual(
+            graph.root_nodes(),
+            set([('app_a', '0001'), ('app_b', '0001'), ('app_c', '0001')]),
+        )
+        self.assertEqual(
+            graph.leaf_nodes(),
+            set([('app_a', '0004'), ('app_b', '0002'), ('app_c', '0002')]),
+        )
 
     def test_circular_graph(self):
         """