Graphs¶
- class sage.categories.graphs.Graphs[source]¶
- Bases: - Category_singleton- The category of graphs. - EXAMPLES: - sage: from sage.categories.graphs import Graphs sage: C = Graphs(); C Category of graphs - >>> 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: from sage.categories.graphs import Graphs sage: C = Graphs().Connected() sage: TestSuite(C).run() - >>> 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: 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] - >>> 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 - selfas a CW complex.- EXAMPLES: - sage: from sage.categories.graphs import Graphs sage: C = Graphs().example() sage: C.dimension() 1 - >>> 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: 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)] 
 - faces()[source]¶
- 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)] - >>> 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: from sage.categories.graphs import Graphs sage: C = Graphs().example() sage: C.facets() [(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)] - >>> 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: 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]