diff --git a/graphkit/functional.py b/graphkit/functional.py
index 65388973..9de470a5 100644
--- a/graphkit/functional.py
+++ b/graphkit/functional.py
@@ -3,6 +3,8 @@
 
 from itertools import chain
 
+from boltons.setutils import IndexedSet as iset
+
 from .base import Operation, NetworkOperation
 from .network import Network
 from .modifiers import optional
@@ -28,7 +30,7 @@ def _compute(self, named_inputs, outputs=None):
 
         result = zip(self.provides, result)
         if outputs:
-            outputs = set(outputs)
+            outputs = sorted(set(outputs))
             result = filter(lambda x: x[0] in outputs, result)
 
         return dict(result)
@@ -185,22 +187,23 @@ def __call__(self, *operations):
 
         # If merge is desired, deduplicate operations before building network
         if self.merge:
-            merge_set = set()
+            merge_set = iset()  # Preseve given node order.
             for op in operations:
                 if isinstance(op, NetworkOperation):
                     net_ops = filter(lambda x: isinstance(x, Operation), op.net.steps)
                     merge_set.update(net_ops)
                 else:
                     merge_set.add(op)
-            operations = list(merge_set)
+            operations = merge_set
 
         def order_preserving_uniquifier(seq, seen=None):
-            seen = seen if seen else set()
+            seen = seen if seen else set()  # unordered, not iterated
             seen_add = seen.add
             return [x for x in seq if not (x in seen or seen_add(x))]
 
         provides = order_preserving_uniquifier(chain(*[op.provides for op in operations]))
-        needs = order_preserving_uniquifier(chain(*[op.needs for op in operations]), set(provides))
+        needs = order_preserving_uniquifier(chain(*[op.needs for op in operations]),
+                                            set(provides))  # unordered, not iterated
 
         # compile network
         net = Network()
diff --git a/graphkit/network.py b/graphkit/network.py
index 0df3ddf8..166693ef 100644
--- a/graphkit/network.py
+++ b/graphkit/network.py
@@ -7,6 +7,8 @@
 
 from io import StringIO
 
+from boltons.setutils import IndexedSet as iset
+
 from .base import Operation
 
 
@@ -107,7 +109,7 @@ def compile(self):
         self.steps = []
 
         # create an execution order such that each layer's needs are provided.
-        ordered_nodes = list(nx.dag.topological_sort(self.graph))
+        ordered_nodes = iset(nx.topological_sort(self.graph))
 
         # add Operations evaluation steps, and instructions to free data.
         for i, node in enumerate(ordered_nodes):
@@ -163,7 +165,7 @@ def _find_necessary_steps(self, outputs, inputs):
         """
 
         # return steps if it has already been computed before for this set of inputs and outputs
-        outputs = tuple(sorted(outputs)) if isinstance(outputs, (list, set)) else outputs
+        outputs = tuple(sorted(outputs)) if isinstance(outputs, (list, set, iset)) else outputs
         inputs_keys = tuple(sorted(inputs.keys()))
         cache_key = (inputs_keys, outputs)
         if cache_key in self._necessary_steps_cache:
@@ -175,7 +177,7 @@ def _find_necessary_steps(self, outputs, inputs):
             # If caller requested all outputs, the necessary nodes are all
             # nodes that are reachable from one of the inputs.  Ignore input
             # names that aren't in the graph.
-            necessary_nodes = set()
+            necessary_nodes = set()  # unordered, not iterated
             for input_name in iter(inputs):
                 if graph.has_node(input_name):
                     necessary_nodes |= nx.descendants(graph, input_name)
@@ -186,7 +188,7 @@ def _find_necessary_steps(self, outputs, inputs):
             # are made unecessary because we were provided with an input that's
             # deeper into the network graph.  Ignore input names that aren't
             # in the graph.
-            unnecessary_nodes = set()
+            unnecessary_nodes = set()  # unordered, not iterated
             for input_name in iter(inputs):
                 if graph.has_node(input_name):
                     unnecessary_nodes |= nx.ancestors(graph, input_name)
@@ -194,7 +196,7 @@ def _find_necessary_steps(self, outputs, inputs):
             # Find the nodes we need to be able to compute the requested
             # outputs.  Raise an exception if a requested output doesn't
             # exist in the graph.
-            necessary_nodes = set()
+            necessary_nodes = set()  # unordered, not iterated
             for output_name in outputs:
                 if not graph.has_node(output_name):
                     raise ValueError("graphkit graph does not have an output "
@@ -266,7 +268,7 @@ def _compute_thread_pool_barrier_method(self, named_inputs, outputs,
         necessary_nodes = self._find_necessary_steps(outputs, named_inputs)
 
         # this keeps track of all nodes that have already executed
-        has_executed = set()
+        has_executed = set()  # unordered, not iterated
 
         # with each loop iteration, we determine a set of operations that can be
         # scheduled, then schedule them onto a thread pool, then collect their
@@ -464,6 +466,7 @@ def ready_to_schedule_operation(op, has_executed, graph):
         A boolean indicating whether the operation may be scheduled for
         execution based on what has already been executed.
     """
+    # unordered, not iterated
     dependencies = set(filter(lambda v: isinstance(v, Operation),
                               nx.ancestors(graph, op)))
     return dependencies.issubset(has_executed)
diff --git a/setup.py b/setup.py
index bd7883f4..46a69077 100644
--- a/setup.py
+++ b/setup.py
@@ -28,7 +28,11 @@
      author_email='huyng@yahoo-inc.com',
      url='http://github.com/yahoo/graphkit',
      packages=['graphkit'],
-     install_requires=['networkx'],
+     install_requires=[
+          "networkx; python_version >= '3.5'",
+          "networkx == 2.2; python_version < '3.5'",
+          "boltons"  # for IndexSet
+     ],
      extras_require={
           'plot': ['pydot', 'matplotlib']
      },