本文整理汇总了Python中sage.graphs.digraph.DiGraph.is_connected方法的典型用法代码示例。如果您正苦于以下问题：Python DiGraph.is_connected方法的具体用法？Python DiGraph.is_connected怎么用？Python DiGraph.is_connected使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类sage.graphs.digraph.DiGraph的用法示例。
在下文中一共展示了DiGraph.is_connected方法的1个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: random_cyclically_reduced_stallings_graph
# 需要导入模块: from sage.graphs.digraph import DiGraph [as 别名]
# 或者: from sage.graphs.digraph.DiGraph import is_connected [as 别名]
def random_cyclically_reduced_stallings_graph(n, r=2, verbose=False, merge=False):
r"""
Return a uniformly chosen Stallings graph of n vertices over r letters.
INPUT:
- ``n`` -- integer, size of graph
- ``r`` -- integer (default: ``2``), number of generators of the free
group
- ``verbose`` -- bool (default: ``False``)
.. NOTE::
The probability that G is connected is 1 - 2^r / n^(r-1) +
o(1/n^(r-1)) which is approx. 1
OUTPUT:
digraph, integer, integer
EXAMPLES::
sage: from slabbe import random_cyclically_reduced_stallings_graph
sage: G,_,_ = random_cyclically_reduced_stallings_graph(20, 2)
sage: G
Looped multi-digraph on 20 vertices
::
sage: random_cyclically_reduced_stallings_graph(20, 5)[0]
Looped multi-digraph on 20 vertices
With verbose output::
sage: G = random_cyclically_reduced_stallings_graph(20, 2, verbose=True) # random
rejecting because graph is not connected
rejecting because graph has a vertex of degree <=1
rejecting because graph has a vertex of degree <=1
rejecting because graph has a vertex of degree <=1
For displaying purposes, the following merges the multiedges
automatically::
sage: G,_,_ = random_cyclically_reduced_stallings_graph(20, 2)
sage: from slabbe import TikzPicture
sage: tikz = TikzPicture.from_graph(G)
sage: _ = tikz.pdf(view=False)
AUTHORS:
- Sébastien Labbé and Pascal Weil, Dec 14, 2017, Sage Thursdays at LaBRI
"""
from sage.misc.latex import LatexExpr
# reject statistics
not_connected_count = 0
has_degree_1_count = 0
while True:
injections = [random_partial_injection(n) for _ in range(r)]
edges = []
for i,injection in enumerate(injections):
label = LatexExpr('a_{}'.format(i))
edges.extend([(j,image_j,label) for (j,image_j) in enumerate(injection)
if not image_j is None])
G = DiGraph([range(n), edges], format='vertices_and_edges',
loops=True, multiedges=True)
if not G.is_connected():
not_connected_count += 1
if verbose:
print("rejecting because graph is not connected")
continue
if not all(d>=2 for d in G.degree_iterator()):
has_degree_1_count += 1
if verbose:
print("rejecting because graph has a vertex of degree <=1")
continue
return G, not_connected_count, has_degree_1_count