diff --git a/stix2/equivalence/graph/__init__.py b/stix2/equivalence/graph/__init__.py
index 3d892f4..402bcb2 100644
--- a/stix2/equivalence/graph/__init__.py
+++ b/stix2/equivalence/graph/__init__.py
@@ -105,31 +105,26 @@ def graph_similarity(ds1, ds2, prop_scores={}, **weight_dict):
         weights,
     )
 
+    weights["_internal"]["ds1"] = ds1
+    weights["_internal"]["ds2"] = ds2
+
     for object1, object2 in pairs:
-        iprop_score1 = {}
-        iprop_score2 = {}
+        iprop_score = {}
         object1_id = object1["id"]
         object2_id = object2["id"]
 
+        result = object_similarity(object1, object2, iprop_score, **weights)
         weights["_internal"]["max_depth"] = depth
-        weights["_internal"]["ds1"] = ds1
-        weights["_internal"]["ds2"] = ds2
-        result1 = object_similarity(object1, object2, iprop_score1, **weights)
-
-        weights["_internal"]["max_depth"] = depth
-        weights["_internal"]["ds1"] = ds2
-        weights["_internal"]["ds2"] = ds1
-        result2 = object_similarity(object2, object1, iprop_score2, **weights)
 
         if object1_id not in results:
-            results[object1_id] = {"lhs": object1_id, "rhs": object2_id, "prop_score": iprop_score1, "value": result1}
-        elif result1 > results[object1_id]["value"]:
-            results[object1_id] = {"lhs": object1_id, "rhs": object2_id, "prop_score": iprop_score1, "value": result1}
+            results[object1_id] = {"lhs": object1_id, "rhs": object2_id, "prop_score": iprop_score, "value": result}
+        elif result > results[object1_id]["value"]:
+            results[object1_id] = {"lhs": object1_id, "rhs": object2_id, "prop_score": iprop_score, "value": result}
 
         if object2_id not in results:
-            results[object2_id] = {"lhs": object2_id, "rhs": object1_id, "prop_score": iprop_score2, "value": result2}
-        elif result2 > results[object2_id]["value"]:
-            results[object2_id] = {"lhs": object2_id, "rhs": object1_id, "prop_score": iprop_score2, "value": result2}
+            results[object2_id] = {"lhs": object2_id, "rhs": object1_id, "prop_score": iprop_score, "value": result}
+        elif result > results[object2_id]["value"]:
+            results[object2_id] = {"lhs": object2_id, "rhs": object1_id, "prop_score": iprop_score, "value": result}
 
     matching_score = sum(x["value"] for x in results.values())
     len_pairs = len(results)
diff --git a/stix2/equivalence/object/__init__.py b/stix2/equivalence/object/__init__.py
index 39eb99a..7f348b6 100644
--- a/stix2/equivalence/object/__init__.py
+++ b/stix2/equivalence/object/__init__.py
@@ -125,12 +125,13 @@ def object_similarity(obj1, obj2, prop_scores={}, **weight_dict):
                         contributing_score = w * comp_funct(obj1["latitude"], obj1["longitude"], obj2["latitude"], obj2["longitude"], threshold)
                     elif comp_funct == reference_check or comp_funct == list_reference_check:
                         max_depth = weights["_internal"]["max_depth"]
-                        if max_depth < 0:
-                            continue  # prevent excessive recursion
+                        if max_depth > 0:
+                            weights["_internal"]["max_depth"] = max_depth - 1
+                            ds1, ds2 = weights["_internal"]["ds1"], weights["_internal"]["ds2"]
+                            contributing_score = w * comp_funct(obj1[prop], obj2[prop], ds1, ds2, **weights)
+                            weights["_internal"]["max_depth"] = max_depth + 1
                         else:
-                            weights["_internal"]["max_depth"] -= 1
-                        ds1, ds2 = weights["_internal"]["ds1"], weights["_internal"]["ds2"]
-                        contributing_score = w * comp_funct(obj1[prop], obj2[prop], ds1, ds2, **weights)
+                            continue  # prevent excessive recursion
                     else:
                         contributing_score = w * comp_funct(obj1[prop], obj2[prop])
 
@@ -376,7 +377,7 @@ def reference_check(ref1, ref2, ds1, ds2, **weights):
     type1, type2 = ref1.split("--")[0], ref2.split("--")[0]
     result = 0.0
 
-    if type1 == type2:
+    if type1 == type2 and type1 in weights:
         if weights["_internal"]["versioning_checks"]:
             result = _versioned_checks(ref1, ref2, ds1, ds2, **weights) / 100.0
         else:
diff --git a/stix2/test/v21/test_environment.py b/stix2/test/v21/test_environment.py
index 80c4ba8..fb651af 100644
--- a/stix2/test/v21/test_environment.py
+++ b/stix2/test/v21/test_environment.py
@@ -723,10 +723,11 @@ def test_object_similarity_different_spec_version_raises():
 
 def test_object_similarity_zero_match():
     IND_KWARGS = dict(
-        indicator_types=["APTX"],
+        indicator_types=["malicious-activity", "bar"],
         pattern="[ipv4-addr:value = '192.168.1.1']",
         pattern_type="stix",
         valid_from="2019-01-01T12:34:56Z",
+        labels=["APTX", "foo"],
     )
     weights = {
         "indicator": {
@@ -742,7 +743,9 @@ def test_object_similarity_zero_match():
     ind1 = stix2.v21.Indicator(id=INDICATOR_ID, **INDICATOR_KWARGS)
     ind2 = stix2.v21.Indicator(id=INDICATOR_ID, **IND_KWARGS)
     env = stix2.Environment().object_similarity(ind1, ind2, **weights)
-    assert round(env) == 0
+    assert round(env) == 8
+    env = stix2.Environment().object_similarity(ind2, ind1, **weights)
+    assert round(env) == 8
 
 
 def test_object_similarity_different_spec_version():
@@ -766,6 +769,9 @@ def test_object_similarity_different_spec_version():
     env = stix2.Environment().object_similarity(ind1, ind2, **weights)
     assert round(env) == 0
 
+    env = stix2.Environment().object_similarity(ind2, ind1, **weights)
+    assert round(env) == 0
+
 
 @pytest.mark.parametrize(
     "refs1,refs2,ret_val", [
@@ -1068,6 +1074,116 @@ def test_graph_similarity_with_filesystem_source(ds, fs):
     assert json.dumps(prop_scores1, sort_keys=True, indent=4) == json.dumps(prop_scores2, sort_keys=True, indent=4)
 
 
+def test_depth_limiting():
+    g1 = [
+        {
+            "type": "foo",
+            "id": "foo--07f9dd2a-1cce-45bb-8cbe-dba3f007aafd",
+            "spec_version": "2.1",
+            "created": "1986-02-08T00:20:17Z",
+            "modified": "1989-12-11T06:54:29Z",
+            "some1_ref": "foo--700a8a3c-9936-412f-b4eb-ede466476180",
+            "some2_ref": "foo--f4a999a3-df94-499d-9cac-6c02e21775ee",
+        },
+        {
+            "type": "foo",
+            "id": "foo--700a8a3c-9936-412f-b4eb-ede466476180",
+            "spec_version": "2.1",
+            "created": "1989-01-06T10:31:54Z",
+            "modified": "1995-06-18T10:25:01Z",
+            "some1_ref": "foo--705afd45-eb56-43fc-a214-313d63d199a3",
+        },
+        {
+            "type": "foo",
+            "id": "foo--705afd45-eb56-43fc-a214-313d63d199a3",
+            "spec_version": "2.1",
+            "created": "1977-11-06T21:19:29Z",
+            "modified": "1997-12-02T20:33:34Z",
+        },
+        {
+            "type": "foo",
+            "id": "foo--f4a999a3-df94-499d-9cac-6c02e21775ee",
+            "spec_version": "2.1",
+            "created": "1991-09-17T00:40:52Z",
+            "modified": "1992-12-06T11:02:47Z",
+            "name": "alice",
+        },
+    ]
+
+    g2 = [
+        {
+            "type": "foo",
+            "id": "foo--71570479-3e6e-48d2-81fb-897454dec55d",
+            "spec_version": "2.1",
+            "created": "1975-12-22T05:20:38Z",
+            "modified": "1980-11-11T01:09:03Z",
+            "some1_ref": "foo--4aeda39b-31fa-4ffb-a847-d8edc175a579",
+            "some2_ref": "foo--941e48d6-3100-4419-9e8c-cf1eb59e71b2",
+        },
+        {
+            "type": "foo",
+            "id": "foo--4aeda39b-31fa-4ffb-a847-d8edc175a579",
+            "spec_version": "2.1",
+            "created": "1976-01-05T08:32:03Z",
+            "modified": "1980-11-09T05:41:02Z",
+            "some1_ref": "foo--689252c3-5d20-43ff-bbf7-c8e45d713768",
+        },
+        {
+            "type": "foo",
+            "id": "foo--689252c3-5d20-43ff-bbf7-c8e45d713768",
+            "spec_version": "2.1",
+            "created": "1974-09-11T18:56:30Z",
+            "modified": "1976-10-31T11:59:43Z",
+        },
+        {
+            "type": "foo",
+            "id": "foo--941e48d6-3100-4419-9e8c-cf1eb59e71b2",
+            "spec_version": "2.1",
+            "created": "1985-01-03T01:07:03Z",
+            "modified": "1992-07-20T21:32:31Z",
+            "name": "alice",
+        }
+    ]
+
+    mem_store1 = stix2.MemorySource(g1)
+    mem_store2 = stix2.MemorySource(g2)
+
+    custom_weights = {
+        "foo": {
+            "some1_ref": (33, stix2.equivalence.object.reference_check),
+            "some2_ref": (33, stix2.equivalence.object.reference_check),
+            "name": (34, stix2.equivalence.object.partial_string_based),
+        },
+        "_internal": {
+            "ignore_spec_version": False,
+            "versioning_checks": False,
+            "max_depth": 1,
+        },
+    }
+    prop_scores1 = {}
+    env1 = stix2.equivalence.graph.graph_similarity(mem_store1, mem_store2, prop_scores1, **custom_weights)
+
+    assert round(env1) == 38
+    assert round(prop_scores1["matching_score"]) == 300
+    assert round(prop_scores1["len_pairs"]) == 8
+    # from 'alice' check in de-reference
+    assert prop_scores1['summary']['foo--71570479-3e6e-48d2-81fb-897454dec55d']['prop_score']['some2_ref']['weight'] == 33
+    assert prop_scores1['summary']['foo--07f9dd2a-1cce-45bb-8cbe-dba3f007aafd']['prop_score']['some2_ref']['weight'] == 33
+
+    # Switching parameters
+    prop_scores2 = {}
+    env2 = stix2.equivalence.graph.graph_similarity(
+        mem_store2, mem_store1, prop_scores2, **custom_weights
+    )
+
+    assert round(env2) == 38
+    assert round(prop_scores2["matching_score"]) == 300
+    assert round(prop_scores2["len_pairs"]) == 8
+    # from 'alice' check in de-reference
+    assert prop_scores2['summary']['foo--71570479-3e6e-48d2-81fb-897454dec55d']['prop_score']['some2_ref']['weight'] == 33
+    assert prop_scores2['summary']['foo--07f9dd2a-1cce-45bb-8cbe-dba3f007aafd']['prop_score']['some2_ref']['weight'] == 33
+
+
 def test_graph_similarity_with_duplicate_graph(ds):
     weights = {
         "_internal": {