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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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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 –  Heike May 6 '12 at 22:26
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Just in case someone wants Heike's link on the web: reference.wolfram.com/mathematica/Combinatorica/ref/Graph.html –  belisarius May 7 '12 at 1:20
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1 Answer

up vote 5 down vote accepted

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]])} &

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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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. >> –  sam84 14 hours ago
    
@sam84, thank you. I will check if i can fix it. –  kguler 13 hours ago
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