diff --git a/src/qibo/backends/__init__.py b/src/qibo/backends/__init__.py
index 73b139c5d9..8bf3309929 100644
--- a/src/qibo/backends/__init__.py
+++ b/src/qibo/backends/__init__.py
@@ -138,12 +138,14 @@ def _default_transpiler(cls):
         qubits = cls._backend.qubits
         natives = cls._backend.natives
         connectivity_edges = cls._backend.connectivity
-        if (
-            qubits is not None
-            and natives is not None
-            and connectivity_edges is not None
-        ):
-            connectivity = nx.Graph(connectivity_edges)
+        if qubits is not None and natives is not None:
+            connectivity = (
+                nx.Graph(connectivity_edges)
+                if connectivity_edges is not None
+                else nx.Graph()
+            )
+            connectivity.add_nodes_from(qubits)
+
             return Passes(
                 connectivity=connectivity,
                 passes=[
@@ -152,7 +154,6 @@ def _default_transpiler(cls):
                     Unroller(NativeGates[natives]),
                 ],
             )
-
         return Passes(passes=[])
 
 
diff --git a/tests/test_backends_global.py b/tests/test_backends_global.py
index dc0b6dfeaa..16ac92d258 100644
--- a/tests/test_backends_global.py
+++ b/tests/test_backends_global.py
@@ -149,7 +149,15 @@ def test_default_transpiler_sim():
     )
 
 
-def test_default_transpiler_hw():
+CONNECTIVITY = [
+    [("A1", "A2"), ("A2", "A3"), ("A3", "A4"), ("A4", "A5")],
+    [("A1", "A2")],
+    [],
+]
+
+
+@pytest.mark.parametrize("connectivity", CONNECTIVITY)
+def test_default_transpiler_hw(connectivity):
     class TempBackend(NumpyBackend):
         def __init__(self):
             super().__init__()
@@ -161,7 +169,7 @@ def qubits(self):
 
         @property
         def connectivity(self):
-            return [("A1", "A2"), ("A2", "A3"), ("A3", "A4"), ("A4", "A5")]
+            return connectivity
 
         @property
         def natives(self):
@@ -172,12 +180,7 @@ def natives(self):
     transpiler = _Global.transpiler()
 
     assert list(transpiler.connectivity.nodes) == ["A1", "A2", "A3", "A4", "A5"]
-    assert list(transpiler.connectivity.edges) == [
-        ("A1", "A2"),
-        ("A2", "A3"),
-        ("A3", "A4"),
-        ("A4", "A5"),
-    ]
+    assert list(transpiler.connectivity.edges) == connectivity
     assert (
         NativeGates.CZ in transpiler.native_gates
         and NativeGates.GPI2 in transpiler.native_gates