diff --git a/python/cugraph/cugraph/dask/structure/mg_property_graph.py b/python/cugraph/cugraph/dask/structure/mg_property_graph.py
index 780c6212797..53f7757eea3 100644
--- a/python/cugraph/cugraph/dask/structure/mg_property_graph.py
+++ b/python/cugraph/cugraph/dask/structure/mg_property_graph.py
@@ -787,7 +787,7 @@ def add_edge_data(
                     self.dst_col_name: dataframe[vertex_col_names[1]].dtype,
                 },
             )
-            temp_dataframe.index.name = self.edge_id_col_name
+            temp_dataframe.index = temp_dataframe.index.rename(self.edge_id_col_name)
             if edge_id_col_name is not None:
                 temp_dataframe.index = temp_dataframe.index.astype(
                     dataframe[edge_id_col_name].dtype
@@ -1331,16 +1331,16 @@ def renumber_vertices_by_type(self, prev_id_column=None):
 
         df = self.__vertex_prop_dataframe
         index_dtype = df.index.dtype
-        if self.__edge_prop_dataframe is not None:
-            # FIXME DASK_CUDF: https://github.com/rapidsai/cudf/issues/11795
-            cat_dtype = df.dtypes[self.type_col_name]
-            df[self.type_col_name] = df[self.type_col_name].astype(str)
-
-            df = df.reset_index().sort_values(by=TCN)
 
-            # FIXME DASK_CUDF: https://github.com/rapidsai/cudf/issues/11795
-            df[self.type_col_name] = df[self.type_col_name].astype(cat_dtype)
+        # FIXME DASK_CUDF: https://github.com/rapidsai/cudf/issues/11795
+        cat_dtype = df.dtypes[TCN]
+        df[TCN] = df[TCN].astype(str)
 
+        # Include self.vertex_col_name when sorting by values to ensure we can
+        # evenly distribute the data across workers.
+        df = df.reset_index().persist()
+        df = df.sort_values(by=[TCN, self.vertex_col_name], ignore_index=True).persist()
+        if self.__edge_prop_dataframe is not None:
             new_name = f"new_{self.vertex_col_name}"
             df[new_name] = 1
             df[new_name] = df[new_name].cumsum() - 1
@@ -1360,6 +1360,9 @@ def renumber_vertices_by_type(self, prev_id_column=None):
             self.__edge_prop_dataframe.index = self.__edge_prop_dataframe.index.astype(
                 edge_index_dtype
             )
+            self.__edge_prop_dataframe.index = self.__edge_prop_dataframe.index.rename(
+                self.edge_id_col_name
+            )
             if prev_id_column is None:
                 df[self.vertex_col_name] = df[new_name]
                 del df[new_name]
@@ -1371,14 +1374,14 @@ def renumber_vertices_by_type(self, prev_id_column=None):
                     }
                 )
         else:
-            if prev_id_column is None:
-                df = df.sort_values(by=self.type_col_name, ignore_index=True)
-            else:
-                df.index.name = prev_id_column
-                df = df.sort_values(by=self.type_col_name).reset_index()
+            if prev_id_column is not None:
+                df[prev_id_column] = df[self.vertex_col_name]
             df[self.vertex_col_name] = 1
             df[self.vertex_col_name] = df[self.vertex_col_name].cumsum() - 1
 
+        # FIXME DASK_CUDF: https://github.com/rapidsai/cudf/issues/11795
+        df[TCN] = df[TCN].astype(cat_dtype)
+
         df[self.vertex_col_name] = df[self.vertex_col_name].astype(index_dtype)
         self.__vertex_prop_dataframe = (
             df.persist().set_index(self.vertex_col_name, sorted=True).persist()
@@ -1424,11 +1427,14 @@ def renumber_edges_by_type(self, prev_id_column=None):
         cat_dtype = df.dtypes[self.type_col_name]
         df[self.type_col_name] = df[self.type_col_name].astype(str)
 
-        if prev_id_column is None:
-            df = df.sort_values(by=self.type_col_name, ignore_index=True)
-        else:
-            df.index = df.index.rename(prev_id_column)
-            df = df.sort_values(by=self.type_col_name).reset_index()
+        # Include self.edge_id_col_name when sorting by values to ensure we can
+        # evenly distribute the data across workers.
+        df = df.reset_index().persist()
+        df = df.sort_values(
+            by=[self.type_col_name, self.edge_id_col_name], ignore_index=True
+        ).persist()
+        if prev_id_column is not None:
+            df[prev_id_column] = df[self.edge_id_col_name]
 
         # FIXME DASK_CUDF: https://github.com/rapidsai/cudf/issues/11795
         df[self.type_col_name] = df[self.type_col_name].astype(cat_dtype)
diff --git a/python/cugraph/cugraph/tests/mg/test_mg_property_graph.py b/python/cugraph/cugraph/tests/mg/test_mg_property_graph.py
index 8978a2a1e5d..88290163ae7 100644
--- a/python/cugraph/cugraph/tests/mg/test_mg_property_graph.py
+++ b/python/cugraph/cugraph/tests/mg/test_mg_property_graph.py
@@ -865,12 +865,13 @@ def test_renumber_vertices_by_type(dataset1_MGPropertyGraph, prev_id_column):
         assert df_id_ranges.loc[key, "start"] == start
         assert df_id_ranges.loc[key, "stop"] == stop
         df = pG.get_vertex_data(types=[key]).compute().to_pandas()
+        df = df.reset_index(drop=True)
         assert len(df) == stop - start + 1
-        assert (df["_VERTEX_"] == cudf.Series(range(start, stop + 1))).all()
+        assert (df["_VERTEX_"] == pd.Series(range(start, stop + 1))).all()
         if prev_id_column is not None:
             cur = df[prev_id_column].sort_values()
             expected = sorted(x for x, *args in data[key][1])
-            assert (cur == cudf.Series(expected, index=cur.index)).all()
+            assert (cur == pd.Series(expected, index=cur.index)).all()
 
     # Make sure we renumber vertex IDs in edge data too
     df = pG.get_edge_data().compute()
@@ -905,8 +906,9 @@ def test_renumber_edges_by_type(dataset1_MGPropertyGraph, prev_id_column):
         assert df_id_ranges.loc[key, "start"] == start
         assert df_id_ranges.loc[key, "stop"] == stop
         df = pG.get_edge_data(types=[key]).compute().to_pandas()
+        df = df.reset_index(drop=True)
         assert len(df) == stop - start + 1
-        assert (df[pG.edge_id_col_name] == cudf.Series(range(start, stop + 1))).all()
+        assert (df[pG.edge_id_col_name] == pd.Series(range(start, stop + 1))).all()
 
         if prev_id_column is not None:
             assert prev_id_column in df.columns