diff --git a/pyzx/graph/base.py b/pyzx/graph/base.py
index 8f6cfec4..c90d0c5b 100644
--- a/pyzx/graph/base.py
+++ b/pyzx/graph/base.py
@@ -142,9 +142,13 @@ def copy(self, adjoint:bool=False, backend:Optional[str]=None) -> 'BaseGraph':
             graph did not.
         """
         from .graph import Graph # imported here to prevent circularity
+        from .multigraph import Multigraph
         if (backend is None):
             backend = type(self).backend
         g = Graph(backend = backend)
+        if isinstance(self, Multigraph) and isinstance(g, Multigraph):
+            g.set_auto_simplify(self._auto_simplify) # type: ignore
+            # mypy issue https://github.com/python/mypy/issues/16413
         g.track_phases = self.track_phases
         g.scalar = self.scalar.copy(conjugate=adjoint)
         g.merge_vdata = self.merge_vdata
@@ -390,14 +394,19 @@ def merge(self, other: 'BaseGraph') -> Tuple[List[VT],List[ET]]:
     def subgraph_from_vertices(self,verts: List[VT]) -> 'BaseGraph':
         """Returns the subgraph consisting of the specified vertices."""
         from .graph import Graph # imported here to prevent circularity
+        from .multigraph import Multigraph
         g = Graph(backend=type(self).backend)
+        if isinstance(self, Multigraph) and isinstance(g, Multigraph):
+            g.set_auto_simplify(self._auto_simplify) # type: ignore
+            # mypy issue https://github.com/python/mypy/issues/16413
         ty = self.types()
         rs = self.rows()
         qs = self.qubits()
         phase = self.phases()
         grounds = self.grounds()
 
-        edges = [self.edge(v,w) for v in verts for w in verts if self.connected(v,w)]
+        edges = [e for e in self.edges() \
+            if self.edge_st(e)[0] in verts and self.edge_st(e)[1] in verts]
 
         vert_map = dict()
         for v in verts:
diff --git a/pyzx/graph/diff.py b/pyzx/graph/diff.py
index 5f22057a..512c51c6 100644
--- a/pyzx/graph/diff.py
+++ b/pyzx/graph/diff.py
@@ -14,9 +14,10 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import copy
 import json
+from collections import Counter
 from typing import Any, Callable, Generic, Optional, List, Dict, Tuple
-import copy
 
 from ..utils import VertexType, EdgeType, FractionLike, FloatInt, phase_to_s
 from .base import BaseGraph, VT, ET
@@ -56,12 +57,11 @@ def calculate_diff(self, g1: BaseGraph[VT,ET], g2: BaseGraph[VT,ET]) -> None:
 		self.new_edges = []
 		self.removed_edges = []
 
-		for e in (new_edges - old_edges):
+		for e in Counter(new_edges - old_edges).elements():
 			self.new_edges.append((g2.edge_st(e), g2.edge_type(e)))
 
-		for e in (old_edges - new_edges):
+		for e in Counter(old_edges - new_edges).elements():
 			s,t = g1.edge_st(e)
-			if s in self.removed_verts or t in self.removed_verts: continue
 			self.removed_edges.append(e)
 
 		for v in new_verts:
@@ -94,8 +94,8 @@ def calculate_diff(self, g1: BaseGraph[VT,ET], g2: BaseGraph[VT,ET]) -> None:
 
 	def apply_diff(self,g: BaseGraph[VT,ET]) -> BaseGraph[VT,ET]:
 		g = copy.deepcopy(g)
-		g.remove_vertices(self.removed_verts)
 		g.remove_edges(self.removed_edges)
+		g.remove_vertices(self.removed_verts)
 		for v in self.new_verts:
 			g.add_vertex_indexed(v)
 			g.set_position(v,*self.changed_pos[v])
diff --git a/pyzx/graph/multigraph.py b/pyzx/graph/multigraph.py
index 7a2541ce..617b683e 100644
--- a/pyzx/graph/multigraph.py
+++ b/pyzx/graph/multigraph.py
@@ -102,11 +102,11 @@ def clone(self) -> 'Multigraph':
         cpy.phase_mult = self.phase_mult.copy()
         cpy.max_phase_index = self.max_phase_index
         return cpy
-    
+
     def set_auto_simplify(self, s: bool):
         """Automatically remove parallel edges as edges are added"""
         self._auto_simplify = s
-    
+
     def multigraph(self):
         return False