diff --git a/graphene/relay/connection.py b/graphene/relay/connection.py
index 1a4684e5..7e03376d 100644
--- a/graphene/relay/connection.py
+++ b/graphene/relay/connection.py
@@ -75,12 +75,23 @@ class Connection(ObjectType):
         edge_class = getattr(cls, "Edge", None)
         _node = node
 
-        class EdgeBase:
-            node = Field(_node, description="The item at the end of the edge")
-            cursor = String(required=True, description="A cursor for use in pagination")
-
         class EdgeMeta:
             description = f"A Relay edge containing a `{base_name}` and its cursor."
+            required = False
+            node_required = False
+
+        if edge_class and hasattr(edge_class, "Meta"):
+            EdgeMeta = type(
+                f"{base_name}EdgeMeta", (getattr(edge_class, "Meta"), EdgeMeta), {}
+            )
+
+        class EdgeBase:
+            node = Field(
+                _node,
+                required=EdgeMeta.node_required,
+                description="The item at the end of the edge",
+            )
+            cursor = String(required=True, description="A cursor for use in pagination")
 
         edge_name = f"{base_name}Edge"
         if edge_class:
@@ -90,6 +101,7 @@ class Connection(ObjectType):
 
         edge = type(edge_name, edge_bases, {"Meta": EdgeMeta})
         cls.Edge = edge
+        edge_field = NonNull(edge) if EdgeMeta.required else edge
 
         options["name"] = name
         _meta.node = node
@@ -101,7 +113,7 @@ class Connection(ObjectType):
                 description="Pagination data for this connection.",
             ),
             "edges": Field(
-                NonNull(List(edge)),
+                NonNull(List(edge_field)),
                 description="Contains the nodes in this connection.",
             ),
         }
diff --git a/graphene/tests/issues/test_968.py b/graphene/tests/issues/test_968.py
new file mode 100644
index 00000000..0d399d44
--- /dev/null
+++ b/graphene/tests/issues/test_968.py
@@ -0,0 +1,90 @@
+from ...types import ObjectType, Field, Schema, String, NonNull
+from ...relay import Connection, ConnectionField
+
+
+def _get_query(_edge_required=False, _node_required=False):
+    class UserPhoto(ObjectType):
+        uri = String()
+
+    class UserPhotosConnection(Connection):
+        class Meta:
+            node = UserPhoto
+
+        class Edge:
+            class Meta:
+                required = _edge_required
+                node_required = _node_required
+
+    class User(ObjectType):
+        name = String(required=True)
+        user_photos = ConnectionField(UserPhotosConnection)
+
+        def resolve_user_photos(self, info):
+            return [UserPhoto(uri="user-1-uri")]
+
+    class Query(ObjectType):
+        user = Field(User)
+
+        def resolve_user(self, info):
+            return User(name="user-1")
+
+    return Query
+
+
+def _get_edge_field(schema):
+    return schema.query.user._type.user_photos._type._meta.fields[
+        "edges"
+    ]._type.of_type.of_type
+
+
+def test_required_nonnull_edge_only():
+    """
+    Test that elements in the edge are required
+    """
+    schema = Schema(query=_get_query(True))
+
+    # Edge
+    assert isinstance(
+        _get_edge_field(schema),
+        NonNull,
+    )
+    # Node
+    assert not isinstance(
+        _get_edge_field(schema).of_type.node._type,
+        NonNull,
+    )
+
+
+def test_required_nonnull_node_only():
+    """
+    Test that elements in the edge are required
+    """
+    schema = Schema(query=_get_query(False, True))
+
+    # Edge
+    assert not isinstance(
+        _get_edge_field(schema),
+        NonNull,
+    )
+    # Node
+    assert isinstance(
+        _get_edge_field(schema).node._type,
+        NonNull,
+    )
+
+
+def test_support_null_nodes():
+    """
+    Test that elements in the edge are required
+    """
+    schema = Schema(query=_get_query())
+
+    assert not isinstance(
+        _get_edge_field(schema),
+        NonNull,
+    )
+
+    assert not isinstance(
+        _get_edge_field(schema).node._type,
+        NonNull,
+    )