#7159: [with patch, needs review] Graph.merge_vertices, and a bug in 
edge_boundary
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   Reporter:  ncohen        |       Owner:  rlm       
       Type:  defect        |      Status:  new       
   Priority:  major         |   Milestone:  sage-4.1.3
  Component:  graph theory  |    Keywords:            
Work_issues:                |      Author:            
   Reviewer:                |      Merged:            
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 This patch adds to the Graph class the function merge_vertices.

 It is a very common operation in Graph Theory. In a Graph G, one merges
 two vertices u and v by deleting them and adding a new vertex, which is
 linked to any other vertex w such that there was an edge uw or vw in G.
 This can be done with any number of vertices at a time.

 Besides, writing this class I noticed there was an error in function
 edge_boundary :

 the function Graph.edge_boundary([u,v]) returns a list of edges, BUT :
     * the edges returned do not always contain u or v as their first
 element. it can be the second one in undirected graphs
     * The edges between u and v are returned, which is not the expected
 behaviour of this function

 This patch fixes this too.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7159>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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