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Can someone provide an example of a Combinatorica-based graph which uses ShowGraph and Graph and takes in an explicitly defined list of edges (not some auto-generated graph). I have not been able to find any documentation which describes the expected input format.

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    $\begingroup$ You can find the input format for the edges and vertices for Combinatorica`Graph under More Information on the page Combinatorica/ref/Graph in the documentation center $\endgroup$ – Heike May 6 '12 at 22:26
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    $\begingroup$ Just in case someone wants Heike's link on the web: reference.wolfram.com/mathematica/Combinatorica/ref/Graph.html $\endgroup$ – Dr. belisarius May 7 '12 at 1:20
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Two examples:

   Needs["Combinatorica`"]
   GraphicsRow[
    {ShowGraph[ 
       g1 = Graph[{{{1, 2}}, {{2, 3}}, {{3, 1}}}, {{{1, 1}}, {{2, 1}}, {{3, 3}}}], 
        VertexNumber -> True], 
     ShowGraph[
      g2 = Graph[
            {{{1, 2}, EdgeLabel -> "lbl1"}, {{2, 3}, EdgeColor -> Green}, 
             {{3, 1}, EdgeLabel -> "(3,1)", EdgeDirection -> True, EdgeLabel -> True, 
                EdgeLabelPosition -> UpperLeft}}, 
           {{{1, 1}, VertexLabel -> True, VertexLabelColor -> Blue, 
   VertexLabelPosition -> LowerRight}, 
             {{2, 1}, VertexNumber -> True, VertexNumberColor -> Orange}, 
             {{3, 3}}}]
    ]}]

to get

enter image description here

EDIT: Before loading Combinatorica you can transform the data using:

   toCombGrphData[gr_] :=  gr // 
       Sequence @@ {EdgeList[#] /. UndirectedEdge[x__] :> {List[x]}, 
                    List /@ (AbsoluteOptions[#, VertexCoordinates][[2]])} &

Update: For Version 9, we need to change the part specification above from [[2]] to [[1,2]] (thanks: @sam84).

Example:

  combgrpg = toCombGrphData[CompleteGraph[3]]

gives the edge list and vertex coordinates needed as input for Combinatorica ``Graph`:

  (*  Sequence[{{{1, 2}}, {{1, 3}}, {{2, 3}}}, {{{0.866025, -0.5}}, {{-0.866025, -0.5}}, {{-2.44929*10^-16, 1.}}}] *)

Then, 

  Needs["Combinatorica`"]

  ShowGraph[Graph[combgrph]]

gives

enter image description here

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  • $\begingroup$ I tried your example in Mathematica 9, but I obtain the following error: Part::partw: Part 2 of {VertexCoordinates->{{-0.866025,-0.5},{0.866025,-0.5},{1.83697*10^-16,1.}}} does not exist. >> $\endgroup$ – sam84 Apr 18 '14 at 17:19
  • $\begingroup$ @sam84, thank you. I will check if i can fix it. $\endgroup$ – kglr Apr 18 '14 at 17:47
  • $\begingroup$ I fixed it. This function works: toCombGrphData[gr_] := gr // Sequence @@ {EdgeList[#] /. UndirectedEdge[x__] :> {List[x]}, List /@ (AbsoluteOptions[#, VertexCoordinates][[1, 2]])} & $\endgroup$ – sam84 Apr 19 '14 at 9:32
  • $\begingroup$ It is possible to extend the function toCombGrphData so to inclue also edge weights? Thanks $\endgroup$ – sam84 Apr 19 '14 at 9:33
  • $\begingroup$ @sam84, can't recall the Combinatorica syntax for using edge weights. If you have simple example handy, perhaps you can post a new question. (Thanks for the fix; I will update the post with the fix.) $\endgroup$ – kglr Apr 19 '14 at 14:46

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