diff --git a/rdflib/graph.py b/rdflib/graph.py
index f90b3acbb..b01d33f82 100644
--- a/rdflib/graph.py
+++ b/rdflib/graph.py
@@ -558,7 +558,10 @@ def __isub__(self, other):
     def __add__(self, other):
         """Set-theoretic union
            BNode IDs are not changed."""
-        retval = Graph()
+        try:
+            retval = type(self)()
+        except TypeError:
+            retval = Graph()
         for (prefix, uri) in set(list(self.namespaces()) + list(other.namespaces())):
             retval.bind(prefix, uri)
         for x in self:
@@ -570,7 +573,10 @@ def __add__(self, other):
     def __mul__(self, other):
         """Set-theoretic intersection.
            BNode IDs are not changed."""
-        retval = Graph()
+        try:
+            retval = type(self)()
+        except TypeError:
+            retval = Graph()
         for x in other:
             if x in self:
                 retval.add(x)
@@ -579,7 +585,10 @@ def __mul__(self, other):
     def __sub__(self, other):
         """Set-theoretic difference.
            BNode IDs are not changed."""
-        retval = Graph()
+        try:
+            retval = type(self)()
+        except TypeError:
+            retval = Graph()
         for x in self:
             if x not in other:
                 retval.add(x)
diff --git a/test/test_graph_operator.py b/test/test_graph_operator.py
new file mode 100644
index 000000000..87502c54b
--- /dev/null
+++ b/test/test_graph_operator.py
@@ -0,0 +1,27 @@
+from rdflib import Graph
+
+
+class MyGraph(Graph):
+    def my_method(self):
+        pass
+
+
+def test_subclass_add_operator():
+    g = MyGraph()
+
+    g = g + g
+    assert "my_method" in dir(g)
+
+
+def test_subclass_sub_operator():
+    g = MyGraph()
+
+    g = g - g
+    assert "my_method" in dir(g)
+
+
+def test_subclass_mul_operator():
+    g = MyGraph()
+
+    g = g * g
+    assert "my_method" in dir(g)