diff --git a/graph/base.py b/graph/base.py
index 94ea70c..8f5c63a 100644
--- a/graph/base.py
+++ b/graph/base.py
@@ -35,6 +35,8 @@ def __eq__(self, other):
             return False
         if self._nodes != other._nodes:
             return False
+        if self._edge_count != other._edge_count:
+            return False
         if self._edges != other._edges:
             return False
         return True
@@ -126,17 +128,16 @@ def del_edge(self, node1, node2):
             del self._edges[node1][node2]
         except KeyError:
             return
+        if not self._edges[node1]:
+            del self._edges[node1]
 
         del self._reverse_edges[node2][node1]
-        self._edge_count -= 1
+        if not self._reverse_edges[node2]:
+            del self._reverse_edges[node2]
 
-        if self._out_degree[node1] == 0:
-            assert False
         self._out_degree[node1] -= 1
-
-        if self._in_degree[node2] == 0:
-            assert False
         self._in_degree[node2] -= 1
+        self._edge_count -= 1
 
     def add_node(self, node_id, obj=None):
         """
@@ -169,18 +170,23 @@ def del_node(self, node_id):
             return
 
         # outgoing
-        for n2, d in self._edges[node_id].copy().items():
+        for n2, _ in self._edges[node_id].copy().items():
             self.del_edge(node_id, n2)
 
         # incoming
-        for n1, d in self._reverse_edges[node_id].copy().items():
+        for n1, _ in self._reverse_edges[node_id].copy().items():
             self.del_edge(n1, node_id)
 
-        del self._edges[node_id]
-        del self._reverse_edges[node_id]  # removes outgoing edges
-        del self._nodes[node_id]
-        del self._in_degree[node_id]
-        del self._out_degree[node_id]
+        for _d in [
+            self._edges, 
+            self._reverse_edges, 
+            self._nodes, 
+            self._in_degree, 
+            self._out_degree]:
+            try:
+                del _d[node_id]
+            except KeyError:
+                pass
 
     def nodes(self, from_node=None, to_node=None, in_degree=None, out_degree=None):
         """
diff --git a/tests/test_basics.py b/tests/test_basics.py
index f946820..bb192ef 100644
--- a/tests/test_basics.py
+++ b/tests/test_basics.py
@@ -230,6 +230,25 @@ def test_in_and_out_degree():
         assert g.in_degree(node) == in_degree[node]
         assert g.out_degree(node) == out_degree[node]
 
+def test_equals():
+    g1 = Graph(from_list=[(1,2),(2,3)])
+    g2 = g1.copy()
+    assert g1 == g2
+
+    g1.add_edge(3,1)
+    g1.del_edge(3,1)
+    assert g1 == g2
+
+    assert g1.edges() == g2.edges()
+    assert g1.nodes() == g2.nodes()
+
+def test_copy_equals():
+    g1 = Graph(from_list=[(1,2),(2,3)])
+    g1.add_edge(3,1)
+    g1.del_edge(3,1)
+    g2 = g1.copy()
+    assert g1 == g2
+
 
 def test_copy():
     g = graph05()