diff --git a/chgnet/graph/graph.py b/chgnet/graph/graph.py
index 5b725d79..90c93508 100644
--- a/chgnet/graph/graph.py
+++ b/chgnet/graph/graph.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 import sys
+from abc import ABC, abstractmethod
 
 from chgnet.utils import write_json
 
@@ -32,13 +33,13 @@ def add_neighbor(self, index, edge):
             self.neighbors[index].append(edge)
 
 
-class UndirectedEdge:
-    """An undirected/bi-directed edge in a graph."""
+class Edge(ABC):
+    """Abstract base class for edges in a graph."""
 
     def __init__(
         self, nodes: list, index: int | None = None, info: dict | None = None
     ) -> None:
-        """Initialize an UndirectedEdge."""
+        """Initialize an Edge."""
         self.nodes = nodes
         self.index = index
         self.info = info
@@ -48,29 +49,40 @@ def __repr__(self):
         nodes, index, info = self.nodes, self.index, self.info
         return f"{type(self).__name__}({nodes=}, {index=}, {info=})"
 
+    def __hash__(self) -> int:
+        """Hash this edge."""
+        img = (self.info or {}).get("image")
+        img_str = "" if img is None else img.tostring()
+        return hash((self.nodes[0], self.nodes[1], img_str))
+
+    @abstractmethod
+    def __eq__(self, other: object) -> bool:
+        """Check if two edges are equal."""
+        raise NotImplementedError
+
+
+class UndirectedEdge(Edge):
+    """An undirected/bi-directed edge in a graph."""
+
+    __hash__ = Edge.__hash__
+
     def __eq__(self, other):
         """Check if two undirected edges are equal."""
         return set(self.nodes) == set(other.nodes) and self.info == other.info
 
 
-class DirectedEdge:
+class DirectedEdge(Edge):
     """A directed edge in a graph."""
 
-    def __init__(
-        self, nodes: list, index: int | None = None, info: dict | None = None
-    ) -> None:
-        """Initialize a DirectedEdge."""
-        self.nodes = nodes
-        self.index = index
-        self.info = info
+    __hash__ = Edge.__hash__
 
-    def make_undirected(self, index, info=None):
+    def make_undirected(self, index: int, info: dict | None = None) -> UndirectedEdge:
         """Make a directed edge undirected."""
         info = info or {}
         info["distance"] = self.info["distance"]
         return UndirectedEdge(self.nodes, index, info)
 
-    def __eq__(self, other) -> bool:
+    def __eq__(self, other: object) -> bool:
         """Check if the two directed edges are equal.
 
         Args:
@@ -80,7 +92,10 @@ def __eq__(self, other) -> bool:
             bool: True if other is the same directed edge, or if other is the directed edge
                 with reverse direction of self, else False.
         """
-        if self.nodes == other.nodes and all(self.info["image"] == other.info["image"]):
+        self_img = (self.info or {}).get("image")
+        other_img = (other.info or {}).get("image")
+        none_img = self_img is other_img is None
+        if self.nodes == other.nodes and (none_img or all(self_img == other_img)):
             # the image key here is provided by Pymatgen, which refers to the periodic
             # cell the neighbor node comes from
 
@@ -94,18 +109,12 @@ def __eq__(self, other) -> bool:
             )
             return True
 
-        return (
-            # In this case the first edge is from node i to j and the second edge is
-            # from node j to i
-            self.nodes == other.nodes[::-1]
-            and (self.info["image"] == -1 * other.info["image"]).all()
+        # In this case the first edge is from node i to j and the second edge is
+        # from node j to i
+        return self.nodes == other.nodes[::-1] and (
+            none_img or all(self_img == -1 * other_img)
         )
 
-    def __repr__(self):
-        """String representation of this edge."""
-        nodes, index, info = self.nodes, self.index, self.info
-        return f"{type(self).__name__}({nodes=}, {index=}, {info=})"
-
 
 class Graph:
     """A graph for storing the neighbor information of atoms."""
diff --git a/tests/test_graph.py b/tests/test_graph.py
index c8b95be6..115f085d 100644
--- a/tests/test_graph.py
+++ b/tests/test_graph.py
@@ -106,8 +106,14 @@ def test_directed_edge() -> None:
     assert edge.index == 0
     assert repr(edge) == f"DirectedEdge(nodes=[0, 1], index=0, {info=})"
 
+    # test hashable
+    _ = {edge}
+
 
 def test_undirected_edge() -> None:
     info = {"image": np.array([0, 0, 0]), "distance": 1.0}
     edge = UndirectedEdge([0, 1], index=0, info=info)
     assert repr(edge) == f"UndirectedEdge(nodes=[0, 1], index=0, {info=})"
+
+    # test hashable
+    _ = {edge}