Graphs#
- class sage.categories.graphs.Graphs(s=None)#
Bases:
Category_singleton
The category of graphs.
EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: C = Graphs(); C Category of graphs
- class Connected(base_category)#
Bases:
CategoryWithAxiom
The category of connected graphs.
EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: C = Graphs().Connected() sage: TestSuite(C).run()
- extra_super_categories()#
Return the extra super categories of
self
.A connected graph is also a metric space.
EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: Graphs().Connected().super_categories() # indirect doctest [Category of connected topological spaces, Category of connected simplicial complexes, Category of graphs, Category of metric spaces]
- class ParentMethods#
Bases:
object
- dimension()#
Return the dimension of
self
as a CW complex.EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: C = Graphs().example() sage: C.dimension() 1
- edges()#
Return the edges of
self
.EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: C = Graphs().example() sage: C.edges() [(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]
- faces()#
Return the faces of
self
.EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: C = Graphs().example() sage: sorted(C.faces(), key=lambda x: (x.dimension(), x.value)) [0, 1, 2, 3, 4, (0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]
- facets()#
Return the facets of
self
.EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: C = Graphs().example() sage: C.facets() [(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]
- vertices()#
Return the vertices of
self
.EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: C = Graphs().example() sage: C.vertices() [0, 1, 2, 3, 4]
- super_categories()#
EXAMPLES:
sage: from sage.categories.graphs import Graphs sage: Graphs().super_categories() [Category of simplicial complexes]