Graphs#

class sage.categories.graphs.Graphs[source]#

Bases: Category_singleton

The category of graphs.

EXAMPLES:

Sage

sage: from sage.categories.graphs import Graphs
sage: C = Graphs(); C
Category of graphs

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs(); C
Category of graphs

class Connected(base_category)[source]#

Bases: CategoryWithAxiom

The category of connected graphs.

EXAMPLES:

Sage

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().Connected()
sage: TestSuite(C).run()

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().Connected()
>>> TestSuite(C).run()

extra_super_categories()[source]#

Return the extra super categories of self.

A connected graph is also a metric space.

EXAMPLES:

Sage

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]

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> 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[source]#

Bases: object

dimension()[source]#

Return the dimension of self as a CW complex.

EXAMPLES:

Sage

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().example()
sage: C.dimension()
1

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example()
>>> C.dimension()
1

edges()[source]#

Return the edges of self.

EXAMPLES:

Sage

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().example()
sage: C.edges()
[(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example()
>>> C.edges()
[(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]

faces()[source]#

Return the faces of self.

EXAMPLES:

Sage

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)]

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example()
>>> 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()[source]#

Return the facets of self.

EXAMPLES:

Sage

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().example()
sage: C.facets()
[(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example()
>>> C.facets()
[(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]

vertices()[source]#

Return the vertices of self.

EXAMPLES:

Sage

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().example()
sage: C.vertices()
[0, 1, 2, 3, 4]

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example()
>>> C.vertices()
[0, 1, 2, 3, 4]

super_categories()[source]#

EXAMPLES:

Sage

sage: from sage.categories.graphs import Graphs
sage: Graphs().super_categories()
[Category of simplicial complexes]

Python

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> Graphs().super_categories()
[Category of simplicial complexes]