trac #34358: clean src/sage/graphs/generic_graph.py - part 4

Author: dcoudert

src/sage/graphs/generic_graph.py

@@ -17605,7 +17605,7 @@ def wiener_index(self, by_weight=False, algorithm=None,
                     G = networkx.Graph(list(self.edges(labels=False, sort=False)))
             G.add_nodes_from(self)
             total = sum(sum(networkx.single_source_dijkstra_path_length(G, u).values())
-                            for u in G)
+                        for u in G)
             WI = total if self.is_directed() else (total / 2)
 
         else:
@@ -17687,14 +17687,14 @@ def average_distance(self, by_weight=False, algorithm=None,
         """
         if self.order() < 2:
             raise ValueError("average distance is not defined for empty or one-element graph")
-        WI =  self.wiener_index(by_weight=by_weight, algorithm=algorithm,
-                                    weight_function=weight_function, check_weight=check_weight)
+        WI = self.wiener_index(by_weight=by_weight, algorithm=algorithm,
+                               weight_function=weight_function, check_weight=check_weight)
         f = 1 if self.is_directed() else 2
         if WI in ZZ:
             return QQ((f * WI, self.order() * (self.order() - 1)))
         return f * WI / (self.order() * (self.order() - 1))
 
-    ### Searches
+    # Searches
 
     def breadth_first_search(self, start, ignore_direction=False,
                              distance=None, neighbors=None,
@@ -18038,7 +18038,7 @@ def depth_first_search(self, start, ignore_direction=False,
                             if x not in seen:
                                 queue.append((w, x, d + 1))
 
-    ### Constructors
+    # Constructors
 
     def add_clique(self, vertices, loops=False):
         """
@@ -18543,7 +18543,9 @@ def cartesian_product(self, other):
             sage: H = Graph([('a', 'b')])
             sage: C1 = G.cartesian_product(H)
             sage: C1.edges(sort=True, labels=None)
-            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'b'), (1, 'b')), ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')), ((1, 'b'), (2, 'b')), ((2, 'a'), (2, 'b'))]
+            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'b'), (1, 'b')),
+             ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')), ((1, 'b'), (2, 'b')),
+             ((2, 'a'), (2, 'b'))]
             sage: C2 = H.cartesian_product(G)
             sage: C1.is_isomorphic(C2)
             True
@@ -18562,7 +18564,16 @@ def cartesian_product(self, other):
             sage: B = digraphs.DeBruijn(['a', 'b'], 2)
             sage: Q = P.cartesian_product(B)
             sage: Q.edges(sort=True, labels=None)
-            [((0, 'aa'), (0, 'aa')), ((0, 'aa'), (0, 'ab')), ((0, 'aa'), (1, 'aa')), ((0, 'ab'), (0, 'ba')), ((0, 'ab'), (0, 'bb')), ((0, 'ab'), (1, 'ab')), ((0, 'ba'), (0, 'aa')), ((0, 'ba'), (0, 'ab')), ((0, 'ba'), (1, 'ba')), ((0, 'bb'), (0, 'ba')), ((0, 'bb'), (0, 'bb')), ((0, 'bb'), (1, 'bb')), ((1, 'aa'), (1, 'aa')), ((1, 'aa'), (1, 'ab')), ((1, 'ab'), (1, 'ba')), ((1, 'ab'), (1, 'bb')), ((1, 'ba'), (1, 'aa')), ((1, 'ba'), (1, 'ab')), ((1, 'bb'), (1, 'ba')), ((1, 'bb'), (1, 'bb'))]
+            [((0, 'aa'), (0, 'aa')), ((0, 'aa'), (0, 'ab')),
+             ((0, 'aa'), (1, 'aa')), ((0, 'ab'), (0, 'ba')),
+             ((0, 'ab'), (0, 'bb')), ((0, 'ab'), (1, 'ab')),
+             ((0, 'ba'), (0, 'aa')), ((0, 'ba'), (0, 'ab')),
+             ((0, 'ba'), (1, 'ba')), ((0, 'bb'), (0, 'ba')),
+             ((0, 'bb'), (0, 'bb')), ((0, 'bb'), (1, 'bb')),
+             ((1, 'aa'), (1, 'aa')), ((1, 'aa'), (1, 'ab')),
+             ((1, 'ab'), (1, 'ba')), ((1, 'ab'), (1, 'bb')),
+             ((1, 'ba'), (1, 'aa')), ((1, 'ba'), (1, 'ab')),
+             ((1, 'bb'), (1, 'ba')), ((1, 'bb'), (1, 'bb'))]
             sage: Q.strongly_connected_components_digraph().num_verts()
             2
             sage: V = Q.strongly_connected_component_containing_vertex((0, 'aa'))
@@ -18709,7 +18720,10 @@ def lexicographic_product(self, other):
             sage: H = Graph([('a', 'b')])
             sage: T = G.lexicographic_product(H)
             sage: T.edges(sort=True, labels=None)
-            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')), ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')), ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')), ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')), ((1, 'b'), (2, 'b')), ((2, 'a'), (2, 'b'))]
+            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')),
+             ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')), ((1, 'a'), (1, 'b')),
+             ((1, 'a'), (2, 'a')), ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')),
+             ((1, 'b'), (2, 'b')), ((2, 'a'), (2, 'b'))]
             sage: T.is_isomorphic(H.lexicographic_product(G))
             False
 
@@ -18719,7 +18733,10 @@ def lexicographic_product(self, other):
             sage: J = DiGraph([('a', 'b')])
             sage: T = I.lexicographic_product(J)
             sage: T.edges(sort=True, labels=None)
-            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')), ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')), ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')), ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')), ((1, 'b'), (2, 'b')), ((2, 'a'), (2, 'b'))]
+            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')),
+             ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')), ((1, 'a'), (1, 'b')),
+             ((1, 'a'), (2, 'a')), ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')),
+             ((1, 'b'), (2, 'b')), ((2, 'a'), (2, 'b'))]
             sage: T.is_isomorphic(J.lexicographic_product(I))
             False
         """
@@ -18861,7 +18878,11 @@ def disjunctive_product(self, other):
             sage: H = Graph([('a', 'b')])
             sage: T = G.disjunctive_product(H)
             sage: T.edges(sort=True, labels=None)
-            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')), ((0, 'a'), (2, 'b')), ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')), ((0, 'b'), (2, 'a')), ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')), ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')), ((1, 'b'), (2, 'b')), ((2, 'a'), (2, 'b'))]
+            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')),
+             ((0, 'a'), (2, 'b')), ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')),
+             ((0, 'b'), (2, 'a')), ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')),
+             ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')), ((1, 'b'), (2, 'b')),
+             ((2, 'a'), (2, 'b'))]
             sage: T.is_isomorphic(H.disjunctive_product(G))
             True
 
@@ -18871,7 +18892,11 @@ def disjunctive_product(self, other):
             sage: J = DiGraph([('a', 'b')])
             sage: T = I.disjunctive_product(J)
             sage: T.edges(sort=True, labels=None)
-            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')), ((0, 'a'), (2, 'b')), ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')), ((1, 'a'), (0, 'b')), ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')), ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')), ((1, 'b'), (2, 'b')), ((2, 'a'), (0, 'b')), ((2, 'a'), (1, 'b')), ((2, 'a'), (2, 'b'))]
+            [((0, 'a'), (0, 'b')), ((0, 'a'), (1, 'a')), ((0, 'a'), (1, 'b')),
+             ((0, 'a'), (2, 'b')), ((0, 'b'), (1, 'a')), ((0, 'b'), (1, 'b')),
+             ((1, 'a'), (0, 'b')), ((1, 'a'), (1, 'b')), ((1, 'a'), (2, 'a')),
+             ((1, 'a'), (2, 'b')), ((1, 'b'), (2, 'a')), ((1, 'b'), (2, 'b')),
+             ((2, 'a'), (0, 'b')), ((2, 'a'), (1, 'b')), ((2, 'a'), (2, 'b'))]
             sage: T.is_isomorphic(J.disjunctive_product(I))
             True
         """
@@ -19047,8 +19072,7 @@ def is_transitively_reduced(self):
 
         return self.is_forest()
 
-
-    ### Visualization
+    # Visualization
 
     def _color_by_label(self, format='hex', as_function=False, default_color="black"):
         """
@@ -19149,7 +19173,8 @@ def _color_by_label(self, format='hex', as_function=False, default_color="black"
             color_of_label = dict(zip(labels, colors))
             color_of_label = color_of_label.__getitem__
         elif isinstance(format, dict):
-            color_of_label = lambda label: format.get(label, default_color)
+            def color_of_label(label):
+                return format.get(label, default_color)
         else:
             # This assumes that ``format`` is already a function
             color_of_label = format
@@ -19218,7 +19243,6 @@ def set_latex_options(self, **kwds):
         opts = self.latex_options()
         opts.set_options(**kwds)
 
-
     def layout(self, layout=None, pos=None, dim=2, save_pos=False, **options):
         """
         Return a layout for the vertices of this graph.
@@ -19341,10 +19365,10 @@ def layout(self, layout=None, pos=None, dim=2, save_pos=False, **options):
             if pos is None:
                 layout = 'default'
 
-        if hasattr(self, "layout_%s"%layout):
-            pos = getattr(self, "layout_%s"%layout)(dim=dim, **options)
+        if hasattr(self, "layout_%s" % layout):
+            pos = getattr(self, "layout_%s" % layout)(dim=dim, **options)
         elif layout is not None:
-            raise ValueError("unknown layout algorithm: %s"%layout)
+            raise ValueError("unknown layout algorithm: %s" % layout)
 
         if len(pos) < self.order():
             pos = self.layout_extend_randomly(pos, dim=dim)
@@ -19353,7 +19377,6 @@ def layout(self, layout=None, pos=None, dim=2, save_pos=False, **options):
             self.set_pos(pos, dim=dim)
         return pos
 
-
     def layout_spring(self, by_component=True, **options):
         """
         Return a spring layout for this graph.
@@ -19490,11 +19513,11 @@ def layout_extend_randomly(self, pos, dim=2):
             sage: (xmin, ymin) == (0, 0) and (xmax, ymax) == (1, 1)
             True
         """
-        assert dim == 2 # 3d not yet implemented
+        assert dim == 2  # 3d not yet implemented
         from sage.misc.randstate import current_randstate
         random = current_randstate().python_random().random
 
-        xmin, xmax,ymin, ymax = self._layout_bounding_box(pos)
+        xmin, xmax, ymin, ymax = self._layout_bounding_box(pos)
 
         dx = xmax - xmin
         dy = ymax - ymin
@@ -19505,7 +19528,6 @@ def layout_extend_randomly(self, pos, dim=2):
                 pos[v] = [xmin + dx * random(), ymin + dy * random()]
         return pos
 
-
     def layout_circular(self, dim=2, center=(0, 0), radius=1, shift=0, angle=0, **options):
         r"""
         Return a circular layout for this graph
@@ -19947,9 +19969,9 @@ def _layout_bounding_box(self, pos):
         ys = [pos[v][1] for v in pos]
         if not xs:
             xmin = -1
-            xmax =  1
+            xmax = 1
             ymin = -1
-            ymax =  1
+            ymax = 1
         else:
             xmin = min(xs)
             xmax = max(xs)
@@ -20047,7 +20069,7 @@ def _circle_embedding(self, vertices, center=(0, 0), radius=1, shift=0, angle=0,
                 pos = self._pos = {}
 
         from math import sin, cos, pi
-        for i,v in enumerate(vertices):
+        for i, v in enumerate(vertices):
             i += shift
             # We round cos and sin to avoid results like 1.2246467991473532e-16
             # when asking for sin(pi)
@@ -20365,7 +20387,11 @@ def plot(self, **options):
 
         ::
 
-            sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []} , sparse=True)
+            sage: D = DiGraph({0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4],
+            ....:              4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14],
+            ....:              8: [9], 9: [10, 13], 10: [11], 11: [12, 18],
+            ....:              12: [16, 13], 13: [14], 14: [15], 15: [16],
+            ....:              16: [17], 17: [18], 18: [19]}, sparse=True)
             sage: for u,v,l in D.edges(sort=False):
             ....:     D.set_edge_label(u, v, '(' + str(u) + ',' + str(v) + ')')
             sage: D.plot(edge_labels=True, layout='circular').show()
@@ -20559,7 +20585,7 @@ def show(self, method="matplotlib", **kwds):
                 return
             from sage.misc.viewer import browser
             import os
-            os.system('%s %s 2>/dev/null 1>/dev/null &'% (browser(), filename))
+            os.system('%s %s 2>/dev/null 1>/dev/null &' % (browser(), filename))
             return
 
         from .graph_plot import graphplot_options