diff --git a/src/sage/combinat/yang_baxter_graph.py b/src/sage/combinat/yang_baxter_graph.py
index 33552e4cc46..3fb02420f27 100644
--- a/src/sage/combinat/yang_baxter_graph.py
+++ b/src/sage/combinat/yang_baxter_graph.py
@@ -15,6 +15,7 @@
 #
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
+from copy import copy
 
 from sage.graphs.digraph import DiGraph
 from sage.structure.sage_object import SageObject
@@ -45,8 +46,8 @@ def YangBaxterGraph(partition=None, root=None, operators=None):
 
     OUTPUT: either:
 
-      - :class:`YangBaxterGraph_partition` -- if partition is defined
-      - :class:`YangBaxterGraph_generic` -- if partition is ``None``
+    - :class:`YangBaxterGraph_partition` -- if partition is defined
+    - :class:`YangBaxterGraph_generic` -- if partition is ``None``
 
     EXAMPLES:
 
@@ -108,8 +109,7 @@ def YangBaxterGraph(partition=None, root=None, operators=None):
     """
     if partition is None:
         return YangBaxterGraph_generic(root=root, operators=operators)
-    else:
-        return YangBaxterGraph_partition(partition=Partition(partition))
+    return YangBaxterGraph_partition(partition=Partition(partition))
 
 # *********** General class for Yang-Baxter Graphs ***********
 
@@ -203,7 +203,7 @@ def _digraph(self):
                 digraph.add_edge(u, v, l)
         return digraph
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         r"""
         TESTS::
 
@@ -236,7 +236,7 @@ def __eq__(self, other) -> bool:
             sage: Y3.__eq__(Y2)
             False
         """
-        return type(self) is type(other) and self._digraph == other._digraph
+        return isinstance(other, YangBaxterGraph_generic) and self._digraph == other._digraph
 
     def __ne__(self, other) -> bool:
         r"""
@@ -311,7 +311,6 @@ def __copy__(self):
             sage: Y == B
             True
         """
-        from copy import copy
         Y = self.__class__(self._root, self._operators)
         Y._digraph = copy(self._digraph)
         return Y
@@ -421,9 +420,7 @@ def vertices(self, sort=False) -> list:
             sage: Y.vertices(sort=True)
             [(0, 2, 1, 0), (2, 0, 1, 0), (2, 1, 0, 0)]
         """
-        if sort:
-            return sorted(self)
-        return list(self)
+        return sorted(self) if sort else list(self)
 
     def edges(self):
         r"""
@@ -505,7 +502,6 @@ def relabel_vertices(self, v, relabel_operator, inplace=True):
             sage: Y.vertices(sort=True)
             [(1, 2, 3, 4), (2, 1, 3, 4), (2, 3, 1, 4)]
         """
-        from copy import copy
         relabelling = self.vertex_relabelling_dict(v, relabel_operator)
         Y = self if inplace else copy(self)
         Y._root = relabelling[Y._root]
@@ -540,11 +536,7 @@ def relabel_edges(self, edge_dict, inplace=True):
             sage: Y.edges()
             [((0, 2, 1, 0), (2, 0, 1, 0), 17), ((2, 0, 1, 0), (2, 1, 0, 0), 27)]
         """
-        if inplace:
-            Y = self
-        else:
-            from copy import copy
-            Y = copy(self)
+        Y = self if inplace else copy(self)
         digraph = Y._digraph
         for u, v in digraph.edges(sort=False, labels=False):
             digraph.set_edge_label(u, v, edge_dict[u, v])
@@ -614,7 +606,6 @@ def __copy__(self):
             sage: Y == B
             True
         """
-        from copy import copy
         Y = self.__class__(self._partition)
         Y._digraph = copy(self._digraph)
         return Y
@@ -634,7 +625,7 @@ def _digraph(self):
             [((0, 1, 0), (1, 0, 0), Swap positions 0 and 1)]
         """
         digraph = super()._digraph
-        for (u, v, op) in digraph.edges(sort=True):
+        for u, v, op in digraph.edges():
             digraph.set_edge_label(u, v, SwapOperator(op.position()))
         return digraph
 
@@ -754,11 +745,10 @@ def relabel_vertices(self, v, inplace=True):
             Y._digraph.relabel(relabelling, inplace=inplace)
             Y._vertex_ordering = Y._digraph.vertices(sort=True)
             return
-        else:
-            from copy import copy
-            Y = copy(self)
-            Y._root = relabelling[Y._root]
-            return Y._digraph.relabel(relabelling, inplace=inplace)
+
+        Y = copy(self)
+        Y._root = relabelling[Y._root]
+        return Y._digraph.relabel(relabelling, inplace=inplace)
 
 # ------------- Some Yang-Baxter operators ------------------
 
@@ -777,7 +767,7 @@ def __init__(self, i):
         """
         self._position = i
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         r"""
         TESTS::
 
@@ -925,9 +915,8 @@ def __call__(self, u):
         j = i + 1
         if u[i] < u[j]:
             v = list(u)
-            (v[j], v[i]) = (v[i], v[j])
+            v[j], v[i] = v[i], v[j]
             if isinstance(u, Permutation):
                 return Permutation(v)
             return type(u)(v)
-        else:
-            return u
+        return u