some ruff fixes and error links in the graphs folder

src/sage/graphs/base/c_graph.pyx

@@ -624,8 +624,8 @@ cdef class CGraph:
 
         OUTPUT:
 
-        - Raise a ``NotImplementedError``. This method is not implemented in
-          this base class. A child class should provide a suitable
+        - Raise a :class:`NotImplementedError`. This method is not implemented
+          in this base class. A child class should provide a suitable
           implementation.
 
         .. SEEALSO::
@@ -1267,7 +1267,7 @@ cdef class CGraph:
 
         OUTPUT:
 
-        - Raise ``NotImplementedError``. This method is not implemented at
+        - Raise :class:`NotImplementedError`. This method is not implemented at
           the :class:`CGraph` level. A child class should provide a suitable
           implementation.
 

src/sage/graphs/base/graph_backends.pyx

@@ -6,7 +6,7 @@ This module implements :class:`GenericGraphBackend` (the base class for
 backends).
 
 Any graph backend must redefine the following methods (for which
-:class:`GenericGraphBackend` raises a ``NotImplementedError``)
+:class:`GenericGraphBackend` raises a :class:`NotImplementedError`)
 
 .. csv-table::
     :class: contentstable

src/sage/graphs/bipartite_graph.py

@@ -1,5 +1,4 @@
 # autopep8: off
-# -*- coding: utf-8 -*-
 r"""
 Bipartite graphs
 

src/sage/graphs/bliss.pyx

@@ -396,9 +396,10 @@ cpdef canonical_form(G, partition=None, return_graph=False, use_edge_labels=True
       canonical graph of ``G`` or its set of edges
 
     - ``use_edge_labels`` -- boolean (default: ``True``); whether to consider
-      edge labels. The edge labels are assumed to be hashable and sortable. If
-      this is not the case (ie a ``TypeError`` is raised), the algorithm will
-      consider the string representations of the labels instead of the labels.
+      edge labels. The edge labels are assumed to be hashable and
+      sortable. If this is not the case (ie a :class:`TypeError` is
+      raised), the algorithm will consider the string representations
+      of the labels instead of the labels.
 
     - ``certificate`` -- boolean (default: ``False``); when set to ``True``,
       returns the labeling of G into a canonical graph

src/sage/graphs/digraph.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Directed graphs
 
@@ -3187,9 +3186,9 @@ def topological_sort(self, implementation="default"):
         """
         Return a topological sort of the digraph if it is acyclic.
 
-        If the digraph contains a directed cycle, a ``TypeError`` is raised. As
-        topological sorts are not necessarily unique, different implementations
-        may yield different results.
+        If the digraph contains a directed cycle, a :class:`TypeError`
+        is raised. As topological sorts are not necessarily unique,
+        different implementations may yield different results.
 
         A topological sort is an ordering of the vertices of the digraph such
         that each vertex comes before all of its successors. That is, if `u`
@@ -3269,7 +3268,8 @@ def topological_sort_generator(self):
         Return an iterator over all topological sorts of the digraph if
         it is acyclic.
 
-        If the digraph contains a directed cycle, a ``TypeError`` is raised.
+        If the digraph contains a directed cycle, a :class:`TypeError`
+        is raised.
 
         A topological sort is an ordering of the vertices of the digraph such
         that each vertex comes before all of its successors. That is, if u comes

src/sage/graphs/digraph_generators.py

@@ -74,7 +74,7 @@
 from sage.graphs.graph import Graph
 
 
-class DiGraphGenerators():
+class DiGraphGenerators:
     r"""
     A class consisting of constructors for several common digraphs,
     including orderly generation of isomorphism class representatives.

src/sage/graphs/domination.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Domination
 

src/sage/graphs/generators/basic.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Basic graphs
 
@@ -400,7 +399,7 @@ def CompleteGraph(n):
         G.set_pos({0: (0, 0)})
     else:
         G._circle_embedding(list(range(n)), angle=pi/2)
-    G.add_edges(((i, j) for i in range(n) for j in range(i + 1, n)))
+    G.add_edges((i, j) for i in range(n) for j in range(i + 1, n))
     return G
 
 def CorrelationGraph(seqs, alpha, include_anticorrelation):

src/sage/graphs/generators/chessboard.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Chessboard graphs
 

src/sage/graphs/generators/degree_sequence.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Graphs with a given degree sequence
 
@@ -98,8 +97,8 @@ def DegreeSequenceBipartite(s1, s2):
         True
 
     Some sequences being incompatible if, for example, their sums are different,
-    the functions raises a ``ValueError`` when no graph corresponding to the
-    degree sequences exists::
+    the functions raises a :class:`ValueError` when no graph corresponding
+    to the degree sequences exists::
 
         sage: g = graphs.DegreeSequenceBipartite([2,2,2,2,1],[5,5])                     # needs sage.combinat sage.modules
         Traceback (most recent call last):

src/sage/graphs/generators/families.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Various families of graphs
 
@@ -594,7 +593,7 @@ def BarbellGraph(n1, n2):
 
     OUTPUT:
 
-    A barbell graph of order ``2*n1 + n2``. A ``ValueError`` is
+    A barbell graph of order ``2*n1 + n2``. A :class:`ValueError` is
     returned if ``n1 < 2`` or ``n2 < 0``.
 
     PLOTTING:
@@ -929,7 +928,7 @@ def BubbleSortGraph(n):
     OUTPUT:
 
     The bubble sort graph `B(n)` on `n` symbols. If `n < 1`, a
-    ``ValueError`` is returned.
+    :class:`ValueError` is returned.
 
     EXAMPLES::
 
@@ -2714,7 +2713,7 @@ def SwitchedSquaredSkewHadamardMatrixGraph(n):
     G = SquaredSkewHadamardMatrixGraph(n).complement()
     G.add_vertex((4 * n - 1)**2)
     G.seidel_switching(list(range((4 * n - 1) * (2 * n - 1))))
-    G.name("switch skewhad^2+*_" + str((n)))
+    G.name("switch skewhad^2+*_" + str(n))
     return G
 
 

src/sage/graphs/generators/intersection.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Intersection graphs
 

src/sage/graphs/generators/platonic_solids.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 1-skeletons of Platonic solids
 

src/sage/graphs/generators/random.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Random graphs
 

src/sage/graphs/generators/smallgraphs.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Various small graphs
 

src/sage/graphs/generators/world_map.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Graphs from the World Map
 

src/sage/graphs/generic_graph.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Generic graphs (common to directed/undirected)
 
@@ -2933,8 +2932,8 @@ def _check_embedding_validity(self, embedding=None, boolean=True):
           ``_embedding``
 
         - ``boolean`` -- boolean (default: ``True``); -- whether to return a
-          boolean answer or raise a ``ValueError`` exception if the embedding is
-          invalid
+          boolean answer or raise a :class:`ValueError` exception
+          if the embedding is invalid
 
         EXAMPLES::
 
@@ -3443,8 +3442,8 @@ def allow_multiple_edges(self, new, check=True, keep_label='any'):
         .. WARNING::
 
             ``'min'`` and ``'max'`` only works if the labels can be compared. A
-            ``TypeError`` might be raised when working with non-comparable
-            objects in Python 3.
+            :class:`TypeError` might be raised when working with non-comparable
+            objects.
 
         EXAMPLES:
 
@@ -4092,7 +4091,7 @@ def density(self):
             if n < 2:
                 return Rational(0)
             if self._directed:
-                return Rational(self.size()) / Rational((n ** 2 - n))
+                return Rational(self.size()) / Rational(n ** 2 - n)
             return Rational(self.size()) / Rational((n ** 2 - n) / 2)
 
     def is_bipartite(self, certificate=False):
@@ -18894,8 +18893,8 @@ def to_simple(self, to_undirected=True, keep_label='any', immutable=None):
         .. WARNING::
 
             ``'min'`` and ``'max'`` only works if the labels can be compared. A
-            ``TypeError`` might be raised when working with non-comparable
-            objects in Python 3.
+            :class:`TypeError` might be raised when working with non-comparable
+            objects.
 
         - ``immutable`` -- boolean (default: ``Non``); whether to create a
           mutable/immutable copy. ``immutable=None`` (default) means that the
@@ -25341,7 +25340,7 @@ def graph_isom_equivalent_non_edge_labeled_graph(g, partition=None, standard_lab
             for el, part in edge_partition:
                 # The multiplicity of a label is the number of edges from u to v
                 # it represents
-                m = sum((y[1] for y in el))
+                m = sum(y[1] for y in el)
                 if m in tmp:
                     tmp[m].append(part)
                 else:

src/sage/graphs/graph.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Undirected graphs
 
@@ -3285,8 +3284,8 @@ def bounded_outdegree_orientation(self, bound, solver=None, verbose=False,
 
         OUTPUT:
 
-        A DiGraph representing the orientation if it exists. A ``ValueError``
-        exception is raised otherwise.
+        A DiGraph representing the orientation if it exists.
+        A :class:`ValueError` exception is raised otherwise.
 
         ALGORITHM:
 

src/sage/graphs/graph_decompositions/modular_decomposition.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Modular Decomposition
 

src/sage/graphs/graph_generators.py

@@ -475,7 +475,7 @@ def wrap_name(x):
 from . import graph
 
 
-class GraphGenerators():
+class GraphGenerators:
     r"""
     A class consisting of constructors for several common graphs, as well as
     orderly generation of isomorphism class representatives. See the

src/sage/graphs/graph_input.py

@@ -559,7 +559,7 @@
         for u in D:
             if len(set(D[u])) != len(D[u]):
                 if multiedges is False:
-                    v = next((v for v in D[u] if D[u].count(v) > 1))
+                    v = next(v for v in D[u] if D[u].count(v) > 1)
                     raise ValueError("non-multigraph got several edges (%s, %s)" % (u, v))
                 multiedges = True
                 break

src/sage/graphs/graph_latex.py

@@ -625,7 +625,7 @@ def set_option(self, option_name, option_value=None):
 
         - ``option_name`` -- a string for a latex option contained in the list
           ``sage.graphs.graph_latex.GraphLatex.__graphlatex_options``.
-          A ``ValueError`` is raised if the option is not allowed.
+          A :class:`ValueError` is raised if the option is not allowed.
 
         - ``option_value`` -- a value for the option.  If omitted, or set to
           ``None``, the option will use the default value.

src/sage/graphs/hypergraph_generators.py

@@ -32,7 +32,7 @@
 """
 
 
-class HypergraphGenerators():
+class HypergraphGenerators:
     r"""
     A class consisting of constructors for common hypergraphs.
     """

src/sage/graphs/lovasz_theta.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 r"""
 Lovász theta-function of graphs
 

src/sage/graphs/pq_trees.py

@@ -558,7 +558,7 @@ def set_contiguous(self, v):
 
         In any case, the sets containing ``v`` are contiguous when this
         function ends. If there is no possibility of doing so, the function
-        raises a ``ValueError`` exception.
+        raises a :class:`ValueError` exception.
 
         EXAMPLES:
 
@@ -837,7 +837,7 @@ def set_contiguous(self, v):
 
         In any case, the sets containing ``v`` are contiguous when this
         function ends. If there is no possibility of doing so, the function
-        raises a ``ValueError`` exception.
+        raises a :class:`ValueError` exception.
 
         EXAMPLES:
 

src/sage/graphs/schnyder.py

@@ -555,7 +555,7 @@ def _compute_coordinates(g, x):
     g.set_pos(coordinates)  # Setting _pos attribute to store coordinates
 
 
-class TreeNode():
+class TreeNode:
     """
     A class to represent each node in the trees used by ``_realizer`` and
     ``_compute_coordinates`` when finding a planar geometric embedding in

src/sage/graphs/tutte_polynomial.py

@@ -218,7 +218,7 @@ def edge_multiplicities(G):
 ########
 
 
-class Ear():
+class Ear:
     r"""
     An ear is a sequence of vertices
 
@@ -372,7 +372,7 @@ def removed_from(self, G):
 ##################
 
 
-class EdgeSelection():
+class EdgeSelection:
     pass