diff --git a/releasenotes/notes/fix-neighbors-deterministic-order-3c8e1a9f4b2d7e05.yaml b/releasenotes/notes/fix-neighbors-deterministic-order-3c8e1a9f4b2d7e05.yaml
new file mode 100644
index 0000000000..b3a221a58a
--- /dev/null
+++ b/releasenotes/notes/fix-neighbors-deterministic-order-3c8e1a9f4b2d7e05.yaml
@@ -0,0 +1,8 @@
+---
+fixes:
+  - |
+    Fixed :meth:`.PyGraph.neighbors`, :meth:`.PyDiGraph.neighbors`, and
+    :meth:`.PyDiGraph.neighbors_undirected` to return neighbors in a
+    deterministic order. Previously, calls to the functions could return
+    nodes in an arbitrary order. See
+    `#1501 <https://github.com/Qiskit/rustworkx/issues/1501>`__.
diff --git a/src/digraph.rs b/src/digraph.rs
index f454dee2f9..fd601d7b90 100644
--- a/src/digraph.rs
+++ b/src/digraph.rs
@@ -1849,8 +1849,8 @@ impl PyDiGraph {
                 .graph
                 .neighbors(NodeIndex::new(node))
                 .map(|node| node.index())
-                .collect::<HashSet<usize>>()
-                .drain()
+                .collect::<IndexSet<usize>>()
+                .drain(..)
                 .collect(),
         }
     }
@@ -1866,7 +1866,7 @@ impl PyDiGraph {
     ///     >>> G.neighbors_undirected(node)
     ///     NodeIndices[3, 1]
     ///     >>> G.to_undirected().neighbors(node)
-    ///     NodeIndices[1, 3]
+    ///     NodeIndices[3, 1]
     ///
     /// For direction-aware neighbors, see :func:`~predecessors` and :func:`~successors`.
     ///
@@ -1881,8 +1881,8 @@ impl PyDiGraph {
                 .graph
                 .neighbors_undirected(NodeIndex::new(node))
                 .map(|node| node.index())
-                .collect::<HashSet<usize>>()
-                .drain()
+                .collect::<IndexSet<usize>>()
+                .drain(..)
                 .collect(),
         }
     }
diff --git a/src/graph.rs b/src/graph.rs
index d9cd17611d..ed54430fc0 100644
--- a/src/graph.rs
+++ b/src/graph.rs
@@ -1186,8 +1186,8 @@ impl PyGraph {
                 .graph
                 .neighbors(NodeIndex::new(node))
                 .map(|node| node.index())
-                .collect::<HashSet<usize>>()
-                .drain()
+                .collect::<indexmap::IndexSet<usize>>()
+                .drain(..)
                 .collect(),
         }
     }
diff --git a/tests/digraph/test_neighbors.py b/tests/digraph/test_neighbors.py
index acd0ee590c..4be041d85d 100644
--- a/tests/digraph/test_neighbors.py
+++ b/tests/digraph/test_neighbors.py
@@ -79,3 +79,27 @@ def test_undirected_neighbors_cycle(self):
             undirected_neighbors = dag.neighbors_undirected(node)
             expected_neighbors = undirected_dag.neighbors(node)
             self.assertEqual(sorted(undirected_neighbors), sorted(expected_neighbors))
+
+    def test_neighbors_deterministic_order(self):
+        # Regression test for https://github.com/Qiskit/rustworkx/issues/1501:
+        # neighbors must be returned in a deterministic order.
+        dag = rustworkx.PyDiGraph()
+        dag.add_nodes_from(range(6))
+        dag.add_edges_from_no_data([(0, 1), (0, 2), (0, 3)])
+        dag.add_edges_from_no_data([(4, 0), (5, 0)])
+        for _ in range(20):
+            self.assertEqual([3, 2, 1], list(dag.neighbors(0)))
+            self.assertEqual([3, 2, 1, 5, 4], list(dag.neighbors_undirected(0)))
+
+    def test_neighbors_dedup_deterministic_order(self):
+        # Parallel edges are deduplicated with a stable order.
+        dag = rustworkx.PyDiGraph()
+        dag.add_nodes_from(["a", "b", "c"])
+        dag.add_edge(0, 1, None)
+        dag.add_edge(0, 1, None)
+        dag.add_edge(0, 2, None)
+        first = list(dag.neighbors(0))
+        self.assertCountEqual([1, 2], first)
+        self.assertEqual(2, len(first))
+        for _ in range(20):
+            self.assertEqual(first, list(dag.neighbors(0)))
diff --git a/tests/graph/test_neighbors.py b/tests/graph/test_neighbors.py
index dca67c2556..e3a81872c9 100644
--- a/tests/graph/test_neighbors.py
+++ b/tests/graph/test_neighbors.py
@@ -41,3 +41,26 @@ def test_no_neighbor(self):
         graph = rustworkx.PyGraph()
         node_a = graph.add_node("a")
         self.assertEqual([], graph.neighbors(node_a))
+
+    def test_neighbors_deterministic_order(self):
+        # Regression test for https://github.com/Qiskit/rustworkx/issues/1501:
+        # neighbors must be returned in a deterministic order.
+        graph = rustworkx.PyGraph()
+        graph.add_nodes_from(range(6))
+        graph.add_edges_from_no_data([(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)])
+        expected = [5, 4, 3, 2, 1]
+        for _ in range(20):
+            self.assertEqual(expected, list(graph.neighbors(0)))
+
+    def test_neighbors_dedup_deterministic_order(self):
+        # Parallel edges are deduplicated, and the surviving order is stable.
+        graph = rustworkx.PyGraph()
+        graph.add_nodes_from(["a", "b", "c"])
+        graph.add_edge(0, 1, None)
+        graph.add_edge(0, 1, None)
+        graph.add_edge(0, 2, None)
+        first = list(graph.neighbors(0))
+        self.assertCountEqual([1, 2], first)
+        self.assertEqual(2, len(first))
+        for _ in range(20):
+            self.assertEqual(first, list(graph.neighbors(0)))