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Re: Adding an edge to a directed cyclic graph

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88962] Re: [mg88908] Adding an edge to a directed cyclic graph
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 22 May 2008 02:38:04 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200805211848.OAA10337@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Aside from explicitly changing the embedding coordinates of vertices in 
the Graph object, offhand the only ways I know to change the location of 
vertices for ShowGraph by Mathematica commands are the Combinatorica 
functions ShakeGraph and SpringEmbedding.  But some other methods are: 
other options are:

   (1) Use GraphPlot instead of ShowGraph and then manually move the 
vertex by clicking in its vicinity until you see a small graphics square 
highlighted, then drag to a new position.

   (2) Use Levon Lloyd's visual graph editor, which exports in 
Combinatorica Graph type form.

Undoubtedly it would not be terribly difficult to construct a Dynamic 
expression that uses locators in order to create and move vertices and 
edges for a graph.  This could just reproduce the behavior of Lloyd's 
visual editor, so it's not clear what would be gained except that 
everything could be done strictly within Mathematica.

You might find helpful the guide to Combinatorica'a graph functions (and 
to the kernel's GraphPlot function) that I used for my Discrete 
Structures course.  See the item "Graphs.nb" on the Files page at:

   www.math.umass.edu/Courses/Math_455_Eisenberg

W_Craig Carter wrote:
> Sorry to ask a question that probably has an answer in the
> Combinatorica book; I've just purchased it and waiting for delivery.
> 
> I am teaching myself discrete math by learning Combinatorica. Is there
> an obvious way to add an edge to a directed graph and have
> the edges renumbered associated with the cyclic order?  The number of
> vertices are fixed.
> 
> This seems like a common thing to do; so before embarking on my own
> code to do this, I am hoping I am missing an obvious built-in.
> 
> For example:
> 
> Needs["Combinatorica`"]
> 
> (*c6 is the cycle in which I'd like to insert and edge*)
> 
> c6 = Cycle[6, Type -> Directed]
> ShowGraph[c6, VertexNumber -> True, EdgeLabel -> True,
>  EdgeLabelColor -> Darker[Orange], BaseStyle -> Large]
> 
> (*here I hope to add a sub-loop to replace the edge going from 4-5*)
> modc6 = AddEdges[
>   DeleteEdge[c6, {4, 5}],
>   {
>    {{4, 5}, EdgeColor -> Green},
>    {{5, 4}, EdgeColor -> Blue},
>    {{4, 5}, EdgeColor -> Red}
>    }
>   ]
> 
> (*the edge numbering no longer corresponds to the cycle index--what I
> need is a "ReplaceEdge"*)
> 
> ShowGraph[modc6, VertexNumber -> True, EdgeLabel -> True,
>  EdgeLabelColor -> Darker[Orange], BaseStyle -> Large]
> 
> (*does anyone know an option to increase the "bowing angle" of the
> Graphics for the subloop?*)
> 
> (*thanks*)

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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