diff --git a/swh/graph/client.py b/swh/graph/client.py
--- a/swh/graph/client.py
+++ b/swh/graph/client.py
@@ -15,6 +15,12 @@
         return "An unexpected error occurred in the Graph backend: {}".format(self.args)
 
 
+class GraphArgumentException(Exception):
+    def __init__(self, *args, response):
+        super().__init__(*args)
+        self.response = response
+
+
 class RemoteGraphClient(RPCClient):
     """Client to the Software Heritage Graph."""
 
@@ -30,6 +36,13 @@
     def get_lines(self, endpoint, **kwargs):
         yield from self.raw_verb_lines("get", endpoint, **kwargs)
 
+    def raise_for_status(self, response) -> None:
+        if response.status_code // 100 == 4:
+            raise GraphArgumentException(
+                response.content.decode("ascii"), response=response
+            )
+        super().raise_for_status(response)
+
     # Web API endpoints
 
     def stats(self):
diff --git a/swh/graph/tests/test_api_client.py b/swh/graph/tests/test_api_client.py
--- a/swh/graph/tests/test_api_client.py
+++ b/swh/graph/tests/test_api_client.py
@@ -2,6 +2,7 @@
 from pytest import raises
 
 from swh.core.api import RemoteException
+from swh.graph.client import GraphArgumentException
 
 
 def test_stats(graph_client):
@@ -288,17 +289,17 @@
 
 
 def test_param_validation(graph_client):
-    with raises(RemoteException) as exc_info:  # SWHID not found
+    with raises(GraphArgumentException) as exc_info:  # SWHID not found
         list(graph_client.leaves("swh:1:ori:fff0000000000000000000000000000000000021"))
     assert exc_info.value.response.status_code == 404
 
-    with raises(RemoteException) as exc_info:  # malformed SWHID
+    with raises(GraphArgumentException) as exc_info:  # malformed SWHID
         list(
             graph_client.neighbors("swh:1:ori:fff000000zzzzzz0000000000000000000000021")
         )
     assert exc_info.value.response.status_code == 400
 
-    with raises(RemoteException) as exc_info:  # malformed edge specificaiton
+    with raises(GraphArgumentException) as exc_info:  # malformed edge specificaiton
         list(
             graph_client.visit_nodes(
                 "swh:1:dir:0000000000000000000000000000000000000016",
@@ -308,7 +309,7 @@
         )
     assert exc_info.value.response.status_code == 400
 
-    with raises(RemoteException) as exc_info:  # malformed direction
+    with raises(GraphArgumentException) as exc_info:  # malformed direction
         list(
             graph_client.visit_nodes(
                 "swh:1:dir:0000000000000000000000000000000000000016",