diff --git a/libpysal/graph/base.py b/libpysal/graph/base.py
index bac254018..821806414 100644
--- a/libpysal/graph/base.py
+++ b/libpysal/graph/base.py
@@ -995,9 +995,13 @@ def isolates(self):
         pandas.Index
             Index with a subset of observations that do not have any neighbor
         """
-        nulls = self._adjacency[self._adjacency == 0].reset_index(level=1)
+        nulls = self._adjacency[self._adjacency == 0]
         # since not all zeros are necessarily isolates, do the focal == neighbor check
-        return nulls[nulls.index == nulls.neighbor].index.unique()
+        return (
+            nulls[nulls.index.codes[0] == nulls.index.codes[1]]
+            .index.get_level_values(0)
+            .unique()
+        )
 
     @cached_property
     def unique_ids(self):
@@ -1399,6 +1403,22 @@ def subgraph(self, ids):
             )
         )
 
+    def eliminate_zeros(self):
+        """Remove graph edges with zero weight
+        Eliminates edges with weight == 0 that do not encode an
+        isolate. This is useful to clean-up edges that will make
+        no effect in operations like :meth:`lag`.
+        Returns
+        -------
+        Graph
+            subset of Graph with zero-weight edges eliminated
+        """
+        # get a mask for isolates
+        isolates = self._adjacency.index.codes[0] == self._adjacency.index.codes[1]
+        # substract isolates from mask of zeros
+        zeros = (self._adjacency == 0) != isolates
+        return Graph(self._adjacency[~zeros], is_sorted=True)
+
 
 def _arrange_arrays(heads, tails, weights, ids=None):
     """
diff --git a/libpysal/graph/tests/test_base.py b/libpysal/graph/tests/test_base.py
index 2dca9b048..3b755abf7 100644
--- a/libpysal/graph/tests/test_base.py
+++ b/libpysal/graph/tests/test_base.py
@@ -942,6 +942,14 @@ def test_component_labels(self):
             expected, nybb.component_labels, check_dtype=False
         )
 
+    def test_eliminate_zeros(self):
+        adj = self.adjacency_str_binary.copy()
+        adj["Bronx", "Queens"] = 0
+        adj["Queens", "Manhattan"] = 0
+        with_zero = graph.Graph(adj)
+        expected = adj.drop([("Bronx", "Queens"), ("Queens", "Manhattan")])
+        pd.testing.assert_series_equal(with_zero.eliminate_zeros()._adjacency, expected)
+
     def test_subgraph(self):
         knn = graph.Graph.build_knn(self.nybb.set_geometry(self.nybb.centroid), k=2)
         sub = knn.subgraph(["Staten Island", "Bronx", "Brooklyn"])