diff --git a/m3gnet/graph/_compute.py b/m3gnet/graph/_compute.py
index a04e88c..4ed7035 100644
--- a/m3gnet/graph/_compute.py
+++ b/m3gnet/graph/_compute.py
@@ -2,7 +2,8 @@
 Computing various graph based operations
 """
 
-from typing import List, Optional, Union
+from __future__ import annotations
+
 import itertools
 
 import numpy as np
@@ -14,7 +15,7 @@
 from ._types import Index, MaterialGraph
 
 
-def _compute_threebody(bond_atom_indices, n_atoms):
+def _compute_threebody(bond_atom_indices: np.array, n_atoms: np.array):
     """
     Calculate the three body indices from pair atom indices
 
@@ -28,14 +29,14 @@ def _compute_threebody(bond_atom_indices, n_atoms):
         n_triple_i (np.ndarray): number of three-body angles each atom
         n_triple_s (np.ndarray): number of three-body angles for each structure
     """
-    n_bond = len(bond_atom_indices)
+    n_bonds = len(bond_atom_indices)
     n_struct = len(n_atoms)
-    n_atom = np.sum(n_atoms)
+    n_atoms_total = np.sum(n_atoms)
 
-    n_bond_per_atom = [np.sum(bond_atom_indices[:, 0] == i) for i in range(n_atom)]
+    n_bond_per_atom = [np.sum(bond_atom_indices[:, 0] == i) for i in range(n_atoms_total)]
 
-    n_triple_i = np.zeros(n_atom, dtype=np.int32)
-    n_triple_ij = np.zeros(n_bond, dtype=np.int32)
+    n_triple_i = np.zeros(n_atoms_total, dtype=np.int32)
+    n_triple_ij = np.zeros(n_bonds, dtype=np.int32)
     n_triple_s = np.zeros(n_struct, dtype=np.int32)
 
     n_triple = 0
@@ -53,8 +54,7 @@ def _compute_threebody(bond_atom_indices, n_atoms):
 
     start = 0
     index = 0
-    for i in range(n_atom):
-        bpa = n_bond_per_atom[i]
+    for i, bpa in enumerate(n_bond_per_atom):
         for j, k in itertools.permutations(range(bpa), 2):
             triple_bond_indices[index] = [start + j, start + k]
             index += 1
@@ -70,7 +70,7 @@ def _compute_threebody(bond_atom_indices, n_atoms):
     return triple_bond_indices, n_triple_ij, n_triple_i, n_triple_s
 
 
-def get_pair_vector_from_graph(graph: List):
+def get_pair_vector_from_graph(graph: list):
     """
     Given a graph list return pair vectors that form the bonds
     Args:
@@ -97,7 +97,7 @@ def get_pair_vector_from_graph(graph: List):
     return tf.cast(diff, DataType.tf_float)
 
 
-def tf_compute_distance_angle(graph: List):
+def tf_compute_distance_angle(graph: list):
     """
     Given a graph with pair, triplet indices, calculate the pair distance,
     triplet angles, etc.
@@ -123,7 +123,7 @@ def tf_compute_distance_angle(graph: List):
     return graph
 
 
-def include_threebody_indices(graph: Union[MaterialGraph, List], threebody_cutoff: Optional[float] = None):
+def include_threebody_indices(graph: MaterialGraph | list, threebody_cutoff: float | None = None):
     """
     Given a graph without threebody indices, add the threebody indices
     according to a threebody cutoff radius
@@ -136,7 +136,7 @@ def include_threebody_indices(graph: Union[MaterialGraph, List], threebody_cutof
     """
     if isinstance(graph, MaterialGraph):
         is_graph = True
-        graph_list: List = graph.as_list()
+        graph_list: list = graph.as_list()
     else:
         is_graph = False
         graph_list = graph
@@ -144,7 +144,7 @@ def include_threebody_indices(graph: Union[MaterialGraph, List], threebody_cutof
     return _list_include_threebody_indices(graph_list, threebody_cutoff=threebody_cutoff, is_graph=is_graph)
 
 
-def _list_include_threebody_indices(graph: List, threebody_cutoff: Optional[float] = None, is_graph: bool = False):
+def _list_include_threebody_indices(graph: list, threebody_cutoff: float | None = None, is_graph: bool = False):
     graph = graph[:]
     bond_atom_indices = graph[Index.BOND_ATOM_INDICES]
     n_bond = bond_atom_indices.shape[0]