Coverage for local/lib/python2.7/site-packages/sage/categories/graphs.py : 94%

""" 

Graphs 

""" 

#***************************************************************************** 

# Copyright (C) 2015 Travis Scrimshaw <tscrim at ucdavis.edu> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#****************************************************************************** 

from sage.misc.abstract_method import abstract_method 

from sage.misc.cachefunc import cached_method 

from sage.categories.category_singleton import Category_singleton 

from sage.categories.simplicial_complexes import SimplicialComplexes 

class Graphs(Category_singleton): 

r""" 

The category of graphs. 

EXAMPLES:: 

sage: from sage.categories.graphs import Graphs 

sage: C = Graphs(); C 

Category of graphs 

TESTS:: 

sage: TestSuite(C).run() 

""" 

@cached_method 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.graphs import Graphs 

sage: Graphs().super_categories() 

[Category of simplicial complexes] 

""" 

return [SimplicialComplexes()] 

class ParentMethods: 

@abstract_method 

def vertices(self): 

""" 

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] 

""" 

@abstract_method 

def edges(self): 

""" 

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)] 

""" 

def dimension(self): 

""" 

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 

""" 

if self.edges(): 

return 1 

return 0 

def facets(self): 

""" 

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)] 

""" 

return self.edges() 

def faces(self): 

""" 

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)] 

""" 

return set(self.edges()).union(self.vertices())