some annotations and pep8 in generic_graph.py

src/sage/graphs/generic_graph.py

@@ -972,10 +972,10 @@ def _latex_(self):
         return self.latex_options().latex()
 
     def tikz(self, format=None, edge_labels=None,
-            color_by_label=False, prog='dot', rankdir='down',
-            standalone_config=None, usepackage=None,
-            usetikzlibrary=None, macros=None,
-            use_sage_preamble=None, **kwds):
+             color_by_label=False, prog='dot', rankdir='down',
+             standalone_config=None, usepackage=None,
+             usetikzlibrary=None, macros=None,
+             use_sage_preamble=None, **kwds):
         r"""
         Return a TikzPicture of the graph.
 
@@ -1133,8 +1133,9 @@ def tikz(self, format=None, edge_labels=None,
                 edge_labels = True
 
         self.latex_options().set_options(format=format,
-                edge_labels=edge_labels, color_by_label=color_by_label,
-                prog=prog, rankdir=rankdir, **kwds)
+                                         edge_labels=edge_labels,
+                                         color_by_label=color_by_label,
+                                         prog=prog, rankdir=rankdir, **kwds)
 
         # by default use sage preamble only for format tkz_graph
         # because content generated by tkz_graph depends on it
@@ -1216,7 +1217,7 @@ def _repr_(self):
             name = self.name() + ": " + name
         return name
 
-    def is_immutable(self):
+    def is_immutable(self) -> bool:
         """
         Check whether the graph is immutable.
 
@@ -1659,14 +1660,14 @@ def export_to_file(self, filename, format=None, **kwds):
         """
         import networkx
 
-        formats = {"adjlist"           : networkx.write_adjlist,
-                   "dot"               : networkx.drawing.nx_pydot.write_dot,
-                   "edgelist"          : networkx.write_edgelist,
-                   "gexf"              : networkx.write_gexf,
-                   "gml"               : networkx.write_gml,
-                   "graphml"           : networkx.write_graphml,
-                   "multiline_adjlist" : networkx.write_multiline_adjlist,
-                   "pajek"             : networkx.write_pajek}
+        formats = {"adjlist": networkx.write_adjlist,
+                   "dot": networkx.drawing.nx_pydot.write_dot,
+                   "edgelist": networkx.write_edgelist,
+                   "gexf": networkx.write_gexf,
+                   "gml": networkx.write_gml,
+                   "graphml": networkx.write_graphml,
+                   "multiline_adjlist": networkx.write_multiline_adjlist,
+                   "pajek": networkx.write_pajek}
 
         if format is None:
             ext = filename[1 + filename.rfind("."):]
@@ -3498,7 +3499,7 @@ def connected(u, v):
                                      "the list associated with {}".format(u, v, u, v))
         return True
 
-    def has_loops(self):
+    def has_loops(self) -> bool:
         """
         Return whether there are loops in the (di)graph.
 
@@ -3542,7 +3543,7 @@ def has_loops(self):
         """
         return self.allows_loops() and any(self.has_edge(v, v) for v in self)
 
-    def allows_loops(self):
+    def allows_loops(self) -> bool:
         """
         Return whether loops are permitted in the (di)graph.
 
@@ -3586,7 +3587,7 @@ def allows_loops(self):
         """
         return self._backend.loops(None)
 
-    def allow_loops(self, new, check=True):
+    def allow_loops(self, new, check=True) -> None:
         """
         Change whether loops are permitted in the (di)graph.
 
@@ -3748,7 +3749,7 @@ def number_of_loops(self):
         """
         return len(self.loop_edges())
 
-    def loop_vertices(self):
+    def loop_vertices(self) -> list:
         """
         Return a list of vertices with loops.
 
@@ -3762,7 +3763,7 @@ def loop_vertices(self):
             return [v for v in self if self.has_edge(v, v)]
         return []
 
-    def has_multiple_edges(self, to_undirected=False):
+    def has_multiple_edges(self, to_undirected=False) -> bool:
         """
         Return whether there are multiple edges in the (di)graph.
 
@@ -3854,7 +3855,7 @@ def has_multiple_edges(self, to_undirected=False):
                             s.add(a)
         return False
 
-    def allows_multiple_edges(self):
+    def allows_multiple_edges(self) -> bool:
         """
         Return whether multiple edges are permitted in the (di)graph.
 
@@ -4221,7 +4222,7 @@ def name(self, new=None):
 
         self._name = str(new)
 
-    def get_pos(self, dim=2):
+    def get_pos(self, dim=2) -> dict:
         """
         Return the position dictionary.
 
@@ -6004,7 +6005,7 @@ def is_planar(self, on_embedding=None, kuratowski=False, set_embedding=False,
             if self.has_multiple_edges() or self.has_loops():
                 raise NotImplementedError("cannot compute with embeddings of multiple-edged or looped graphs")
             elif (self.is_directed() and
-                      any(self.has_edge(v, u) for u, v in self.edge_iterator(labels=False))):
+                  any(self.has_edge(v, u) for u, v in self.edge_iterator(labels=False))):
                 raise NotImplementedError("cannot compute with embeddings of digraphs with pairs of opposite arcs")
 
         if on_embedding is not None:
@@ -6488,15 +6489,15 @@ def layout_planar(self, set_embedding=False, on_embedding=None,
         _compute_coordinates(G, tree_nodes)
 
         # Delete all the edges added to the graph
-        #G.delete_edges( extra_edges )
-        #self.delete_edges( other_added_edges )
+        # G.delete_edges( extra_edges )
+        # self.delete_edges( other_added_edges )
 
         if embedding_copy is not None:
             self._embedding = embedding_copy
 
         return G._pos
 
-    def is_drawn_free_of_edge_crossings(self):
+    def is_drawn_free_of_edge_crossings(self) -> bool:
         """
         Check whether the position dictionary for this graph is set and that
         position dictionary gives a planar embedding.
@@ -8944,13 +8945,13 @@ def longest_path(self, s=None, t=None, use_edge_labels=False,
         #   the two in a directed graph (the graph is connected).
         if (self.order() <= 1 or
             (s is not None and (
-                    (s not in self) or
-                    (self._directed and not self.out_degree(s)) or
-                    (not self._directed and not self.degree(s)))) or
+                (s not in self) or
+                (self._directed and not self.out_degree(s)) or
+                (not self._directed and not self.degree(s)))) or
             (t is not None and (
-                    (t not in self) or
-                    (self._directed and not self.in_degree(t)) or
-                    (not self._directed and not self.degree(t)))) or
+                (t not in self) or
+                (self._directed and not self.in_degree(t)) or
+                (not self._directed and not self.degree(t)))) or
             (self._directed and (s is not None) and (t is not None) and
              not self.shortest_path(s, t))):
             if self._directed:
@@ -9658,7 +9659,7 @@ def weight(label):
                                  (vv, uu, self.edge_label(vv, uu))]
                     answer = self.subgraph(edges=edges, immutable=self.is_immutable())
                     answer.set_pos(self.get_pos())
-                    answer._name = "TSP from "+self.name()
+                    answer._name = "TSP from " + self.name()
                     return answer
             elif self.allows_multiple_edges() and len(self.edge_label(uu, vv)) > 1:
                 if maximize:
@@ -11818,7 +11819,7 @@ def delete_vertices(self, vertices):
 
         self._backend.del_vertices(vertices)
 
-    def has_vertex(self, vertex):
+    def has_vertex(self, vertex) -> bool:
         """
         Check if ``vertex`` is one of the vertices of this graph.
 
@@ -13326,7 +13327,7 @@ def set_edge_label(self, u, v, l):
                                    "multiple edges from %s to %s" % (u, v))
         self._backend.set_edge_label(u, v, l, self._directed)
 
-    def has_edge(self, u, v=None, label=None):
+    def has_edge(self, u, v=None, label=None) -> bool:
         r"""
         Check whether ``(u, v)`` is an edge of the (di)graph.
 
@@ -15292,7 +15293,7 @@ def subgraph_decompositions(self, H, induced=False):
         from sage.combinat.matrices.dancing_links import dlx_solver
 
         edges = list(self.edges(labels=False))
-        edge_to_column_id = {edge:i for i, edge in enumerate(edges)}
+        edge_to_column_id = {edge: i for i, edge in enumerate(edges)}
 
         rows = set()
         for h in self.subgraph_search_iterator(H, induced=induced, return_graphs=True):
@@ -19427,9 +19428,9 @@ def breadth_first_search(self, start, ignore_direction=False,
         if (neighbors is None and not isinstance(start, list) and distance is None
                 and hasattr(self._backend, "breadth_first_search")):
             yield from self._backend.breadth_first_search(
-                    start, ignore_direction=ignore_direction,
-                    report_distance=report_distance, edges=edges,
-                    forbidden_vertices=forbidden_vertices)
+                start, ignore_direction=ignore_direction,
+                report_distance=report_distance, edges=edges,
+                forbidden_vertices=forbidden_vertices)
         else:
             if neighbors is None:
                 if not self._directed or ignore_direction:
@@ -22000,7 +22001,7 @@ def layout_tutte(self, external_face=None, external_face_pos=None, **options):
                     M[i, j] = -1
                 M[i, i] = len(nv)
 
-        sol = M.pseudoinverse()*b
+        sol = M.pseudoinverse() * b
         return dict(zip(self, sol))
 
     def _layout_bounding_box(self, pos):
@@ -22125,11 +22126,11 @@ def _circle_embedding(self, vertices, center=(0, 0), radius=1, shift=0, angle=0,
 
         from math import cos, pi, sin
         for i, v in enumerate(vertices):
-            i += shift
+            theta = angle + 2 * (i + shift) * pi / n
             # We round cos and sin to avoid results like 1.2246467991473532e-16
             # when asking for sin(pi)
-            v_x = c_x + radius * round(cos(angle + 2*i*pi / n), 10)
-            v_y = c_y + radius * round(sin(angle + 2*i*pi / n), 10)
+            v_x = c_x + radius * round(cos(theta), 10)
+            v_y = c_y + radius * round(sin(theta), 10)
             pos[v] = (v_x, v_y)
 
         if return_dict:
@@ -22857,14 +22858,14 @@ def plot3d(self, bgcolor=(1, 1, 1),
                     R = rainbow(l)
                     vertex_colors = {R[i]: partition[i] for i in range(l)}
                 else:
-                    vertex_colors = {(1, 0, 0) : list(self)}
+                    vertex_colors = {(1, 0, 0): list(self)}
 
             if color_by_label:
                 if edge_colors is None:
                     # do the coloring
                     edge_colors = self._color_by_label(format=color_by_label)
             elif edge_colors is None:
-                edge_colors = {(0, 0, 0) : self.edges(sort=False)}
+                edge_colors = {(0, 0, 0): self.edges(sort=False)}
 
             # by default turn off the frame
             if 'frame' not in kwds:
@@ -22907,7 +22908,7 @@ def plot3d(self, bgcolor=(1, 1, 1),
                     edge_colors = self._color_by_label(format=color_by_label)
 
             if edge_colors is None:
-                edge_colors = {(0, 0, 0) : self.edges(sort=False)}
+                edge_colors = {(0, 0, 0): self.edges(sort=False)}
 
             i = 0
 
@@ -22916,7 +22917,7 @@ def plot3d(self, bgcolor=(1, 1, 1),
                 TT.texture('edge_color_%d' % i, ambient=0.1, diffuse=0.9,
                            specular=0.03, opacity=1.0, color=color)
                 if self._directed:
-                    for u,v,l in edge_colors[color]:
+                    for u, v, l in edge_colors[color]:
                         TT.fcylinder((pos3d[u][0], pos3d[u][1], pos3d[u][2]),
                                      (pos3d[v][0], pos3d[v][1], pos3d[v][2]),
                                      edge_size, 'edge_color_%d' % i)
@@ -23606,7 +23607,7 @@ def graphviz_string(self, **options):
             color_by_edge = {}
             for color in options['edge_colors'].keys():
                 for edge in options['edge_colors'][color]:
-                    assert isinstance(edge, (list, tuple)) and len(edge) >= 2 and len(edge) <= 3,\
+                    assert isinstance(edge, (list, tuple)) and len(edge) >= 2 and len(edge) <= 3, \
                         "%s is not a valid format for edge" % (edge)
                     u = edge[0]
                     v = edge[1]
@@ -23668,10 +23669,10 @@ def graphviz_string(self, **options):
                 'backward': False,
                 'dot': None,
                 'edge_string': default_edge_string,
-                'color' : default_color,
-                'label' : label,
+                'color': default_color,
+                'label': label,
                 'label_style': options['labels'] if options['edge_labels'] else None
-                }
+            }
             for f in edge_option_functions:
                 edge_options.update(f((u, v, label)))
 
@@ -25047,8 +25048,10 @@ def is_vertex_transitive(self, partition=None, verbosity=0,
                 return False
 
         new_partition = self.automorphism_group(partition,
-                          verbosity=verbosity, edge_labels=edge_labels,
-                          order=False, return_group=False, orbits=True)
+                                                verbosity=verbosity,
+                                                edge_labels=edge_labels,
+                                                order=False,
+                                                return_group=False, orbits=True)
 
         return (len(partition) == len(new_partition))
 
@@ -25904,7 +25907,7 @@ def is_cayley(self, return_group=False, mapping=False,
                 else:
                     c = C[0].is_cayley(return_group=False)
         elif (not self.allows_loops() and not self.allows_multiple_edges() and
-              self.density() > Rational(1)/Rational(2)):
+              self.density() > Rational(1) / Rational(2)):
             if certificate:
                 c, G = self.complement().is_cayley(return_group=True,
                                                    allow_disconnected=True)
@@ -26201,7 +26204,7 @@ def katz_matrix(self, alpha, nonedgesonly=False, vertices=None):
 
         if spectral_radius == 0:
             raise ValueError('the spectral radius of the graph must not be zero')
-        if alpha >= 1/spectral_radius:
+        if alpha >= 1 / spectral_radius:
             raise ValueError('the parameter alpha must be less than the reciprocal of the spectral radius of the graph')
 
         In = matrix.identity(n)