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]