#7571: use more dicts in graph.py
----------------------------+-----------------------------------------------
   Reporter:  ylchapuy      |       Owner:  rlm               
       Type:  enhancement   |      Status:  new               
   Priority:  major         |   Milestone:  sage-4.3          
  Component:  graph theory  |    Keywords:                    
Work_issues:                |      Author:  Yann Laigle-Chapuy
   Upstream:  N/A           |    Reviewer:                    
     Merged:                |  
----------------------------+-----------------------------------------------

Comment(by ylchapuy):

 for the record:

 Before:
 {{{
 sage: g=graphs.RandomGNP(10000,.00011)
 sage: time g.girth()
 CPU times: user 8.19 s, sys: 0.02 s, total: 8.20 s
 Wall time: 8.21 s
 33
 sage: time g.connected_components_number()
 CPU times: user 2.06 s, sys: 0.00 s, total: 2.07 s
 Wall time: 2.09 s
 4474
 sage: g=g.connected_components_subgraphs()[0]
 sage: len(g)
 1784
 sage: time b=g.blocks_and_cut_vertices()
 CPU times: user 0.28 s, sys: 0.00 s, total: 0.28 s
 Wall time: 0.28 s
 }}}

 After:
 {{{
 sage: g=graphs.RandomGNP(10000,.00011)
 sage: time g.girth()
 CPU times: user 5.00 s, sys: 0.00 s, total: 5.00 s
 Wall time: 5.00 s
 33
 sage: time g.connected_components_number()
 CPU times: user 0.20 s, sys: 0.00 s, total: 0.20 s
 Wall time: 0.20 s
 4487
 sage: g=g.connected_components_subgraphs()[0]
 sage: len(g)
 2509
 sage: time b=g.blocks_and_cut_vertices()
 CPU times: user 0.16 s, sys: 0.00 s, total: 0.16 s
 Wall time: 0.16 s
 }}}

 And more importantly:
 {{{
 sage: g = graphs.KrackhardtKiteGraph()
 sage: g.relabel(map(lambda i: 'x'+str(i),range(len(g))))
 }}}

 before:
 {{{
 sage: g.blocks_and_cut_vertices()
 ([[9, 8], [8, 7], [7, 4, 6, 5, 2, 3, 1, 0]], [8, 7])
 }}}

 after:
 {{{
 sage: g.blocks_and_cut_vertices()

 ([['x9', 'x8'],
   ['x5', 'x4', 'x1', 'x0', 'x2', 'x3', 'x6', 'x7'],
   ['x7', 'x8']],
  ['x8', 'x7'])
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7571#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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