Examples of graphs#

class sage.categories.examples.graphs.Cycle(n=5)[source]#

Bases: UniqueRepresentation, Parent

An example of a graph: the cycle of length \(n\).

This class illustrates a minimal implementation of a graph.

EXAMPLES:

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().example(); C
An example of a graph: the 5-cycle

sage: C.category()
Category of graphs

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example(); C
An example of a graph: the 5-cycle

>>> C.category()
Category of graphs

We conclude by running systematic tests on this graph:

sage: TestSuite(C).run()

>>> from sage.all import *
>>> TestSuite(C).run()
class Element[source]#

Bases: ElementWrapper

dimension()[source]#

Return the dimension of self.

EXAMPLES:

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().example()
sage: e = C.edges()[0]
sage: e.dimension()
2
sage: v = C.vertices()[0]
sage: v.dimension()
1

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example()
>>> e = C.edges()[Integer(0)]
>>> e.dimension()
2
>>> v = C.vertices()[Integer(0)]
>>> v.dimension()
1
an_element()[source]#

Return an element of the graph, as per Sets.ParentMethods.an_element().

EXAMPLES:

sage: from sage.categories.graphs import Graphs
sage: C = Graphs().example()
sage: C.an_element()
0

>>> from sage.all import *
>>> from sage.categories.graphs import Graphs
>>> C = Graphs().example()
>>> C.an_element()
0
edges()[source]#

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)]

>>> 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)]
vertices()[source]#

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]

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

alias of Cycle