diff --git a/_nx_arangodb/VERSION b/_nx_arangodb/VERSION
index 1cc5f65..8cfbc90 100644
--- a/_nx_arangodb/VERSION
+++ b/_nx_arangodb/VERSION
@@ -1 +1 @@
-1.1.0
\ No newline at end of file
+1.1.1
\ No newline at end of file
diff --git a/nx_arangodb/convert.py b/nx_arangodb/convert.py
index 09cfa97..8eda47b 100644
--- a/nx_arangodb/convert.py
+++ b/nx_arangodb/convert.py
@@ -138,11 +138,11 @@ def _to_nxcg_graph(G: Any, as_directed: bool = False) -> nxcg.Graph:
             return G
 
         if isinstance(G, nxadb.Graph):
+            logger.debug("converting nx_arangodb graph to nx_cugraph graph")
+
             if not G.graph_exists_in_db:
-                m = "nx_arangodb.Graph does not exist in ArangoDB. Cannot pull graph."
-                raise ValueError(m)
+                return nxcg.convert.from_networkx(G)
 
-            logger.debug("converting nx_arangodb graph to nx_cugraph graph")
             return nxadb_to_nxcg(G, as_directed=as_directed)
 
         raise TypeError(f"Expected nx_arangodb.Graph or nxcg.Graph; got {type(G)}")
diff --git a/nx_arangodb/interface.py b/nx_arangodb/interface.py
index 4704875..c756a32 100644
--- a/nx_arangodb/interface.py
+++ b/nx_arangodb/interface.py
@@ -62,13 +62,15 @@ def _auto_func(func_name: str, /, *args: Any, **kwargs: Any) -> Any:
     """
     dfunc = _registered_algorithms[func_name]
 
-    backend_priority = []
+    backend_priority: list[str] = []
     if nxadb.convert.GPU_AVAILABLE and nx.config.backends.arangodb.use_gpu:
         backend_priority.append("cugraph")
 
     for backend in backend_priority:
-        if not dfunc.__wrapped__._should_backend_run(backend, *args, **kwargs):
-            logger.warning(f"'{func_name}' cannot be run on backend '{backend}'")
+        if not _should_backend_run(backend, dfunc, *args, **kwargs):
+            continue
+
+        if not _can_backend_run(backend, dfunc, *args, **kwargs):
             continue
 
         try:
@@ -80,7 +82,7 @@ def _auto_func(func_name: str, /, *args: Any, **kwargs: Any) -> Any:
             )
 
         except NotImplementedError:
-            logger.warning(f"'{func_name}' not implemented for backend '{backend}'")
+            logger.debug(f"'{func_name}' not implemented for backend '{backend}'")
             pass
 
     default_backend = "networkx"
@@ -88,6 +90,32 @@ def _auto_func(func_name: str, /, *args: Any, **kwargs: Any) -> Any:
     return _run_with_backend(default_backend, dfunc, args, kwargs)
 
 
+def _should_backend_run(backend: str, dfunc: Any, *args: Any, **kwargs: Any) -> bool:
+    """Wrapper around NetworkX's should_backend_run function, because
+    the signature is different for NetworkX <=3.3 and 3.4:
+
+    - https://github.com/networkx/networkx/blob/networkx-3.3/networkx/utils/backends.py#L821  # noqa: E501
+    - https://github.com/networkx/networkx/blob/networkx-3.4.1/networkx/utils/backends.py#L1514  # noqa: E501
+    """
+    try:
+        return bool(dfunc.__wrapped__._should_backend_run(backend, *args, **kwargs))
+    except TypeError:
+        return bool(dfunc.__wrapped__._should_backend_run(backend, args, kwargs))
+
+
+def _can_backend_run(backend: str, dfunc: Any, *args: Any, **kwargs: Any) -> bool:
+    """Wrapper around NetworkX's _can_backend_run function, because
+    the signature is different for NetworkX <=3.3 and 3.4:
+
+    - https://github.com/networkx/networkx/blob/networkx-3.3/networkx/utils/backends.py#L810  # noqa: E501
+    - https://github.com/networkx/networkx/blob/networkx-3.4.1/networkx/utils/backends.py#L1489  # noqa: E501
+    """
+    try:
+        return bool(dfunc.__wrapped__._can_backend_run(backend, *args, **kwargs))
+    except TypeError:
+        return bool(dfunc.__wrapped__._can_backend_run(backend, args, kwargs))
+
+
 def _run_with_backend(
     backend_name: str,
     dfunc: NetworkXFunction,
diff --git a/pyproject.toml b/pyproject.toml
index b804121..35aa776 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -28,7 +28,7 @@ classifiers = [
     "Topic :: Software Development :: Libraries :: Python Modules",
 ]
 dependencies = [
-    "networkx>=3.0,<=3.3",
+    "networkx>=3.0,<=3.4",
     "phenolrs~=0.5",
     "python-arango~=8.1",
     "adbnx-adapter~=5.0.5"