Get complete graph from set of vertices?












3












$begingroup$


There is a function in Mathematica called CompleteGraph which takes a number and makes a complete graph with that number of vertices:



CompleteGraph[5]



enter image description here




However, in the above the vertices become labelled {1,2,3,4,5}. In contrast, given a set of vertices like e.g.,



vertices={1,3,5,6,8};


I would like to get a complete graph in which the vertices are labelled by the above labels. Is it possible to do that quickly (computationally efficiently) in Mathematica?






function-construction graphs-and-networks







share|improve this question









$endgroup$

















    3












    $begingroup$


    There is a function in Mathematica called CompleteGraph which takes a number and makes a complete graph with that number of vertices:



    CompleteGraph[5]



    enter image description here




    However, in the above the vertices become labelled {1,2,3,4,5}. In contrast, given a set of vertices like e.g.,



    vertices={1,3,5,6,8};


    I would like to get a complete graph in which the vertices are labelled by the above labels. Is it possible to do that quickly (computationally efficiently) in Mathematica?






    function-construction graphs-and-networks







    share|improve this question









    $endgroup$















      3












      3








      3





      $begingroup$


      There is a function in Mathematica called CompleteGraph which takes a number and makes a complete graph with that number of vertices:



      CompleteGraph[5]



      enter image description here




      However, in the above the vertices become labelled {1,2,3,4,5}. In contrast, given a set of vertices like e.g.,



      vertices={1,3,5,6,8};


      I would like to get a complete graph in which the vertices are labelled by the above labels. Is it possible to do that quickly (computationally efficiently) in Mathematica?






      function-construction graphs-and-networks







      share|improve this question









      $endgroup$




      There is a function in Mathematica called CompleteGraph which takes a number and makes a complete graph with that number of vertices:



      CompleteGraph[5]



      enter image description here




      However, in the above the vertices become labelled {1,2,3,4,5}. In contrast, given a set of vertices like e.g.,



      vertices={1,3,5,6,8};


      I would like to get a complete graph in which the vertices are labelled by the above labels. Is it possible to do that quickly (computationally efficiently) in Mathematica?






      function-construction graphs-and-networks




      function-construction graphs-and-networks






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 10 hours ago









      KagaratschKagaratsch

      4,64831247




      4,64831247






















          2 Answers
          2






          active

          oldest

          votes


















          2












          $begingroup$

          Graph[UndirectedEdge @@@ Subsets[vertices, {2}], VertexLabels -> "Name"]


          enter image description here



          Alternatively, you can use any of the following to get the same result:



          SimpleGraph[RelationGraph[True &, vertices], VertexLabels -> "Name"]
          
AdjacencyGraph[vertices, ConstantArray[1, {5,5}]-IdentityMatrix[5], VertexLabels -> "Name"]
          
SetProperty[VertexReplace[#, Thread[VertexList@# -> vertices]] &@ CompleteGraph[5],
          
  VertexLabels -> "Name"]


          To change just the labels you can use:



          CompleteGraph[5, VertexLabels -> {k_ :> vertices[[k]]}]



          same picture







          share|improve this answer











          $endgroup$













          • $begingroup$
            The first CompleteGraph approach seems to only change the labels but not the vertex names. The other two versions work great, thank you! (True, I guess my question was asking about labels, sorry for the confusion.)
            $endgroup$
            – Kagaratsch
            10 hours ago












          • $begingroup$
            @Kagaratsch, my pleasure. Thank you for the accept.
            $endgroup$
            – kglr
            10 hours ago



















          1












          $begingroup$

          Another way is with AdjacencyGraph.



          SimpleGraph[
          
 AdjacencyGraph[vertices, ConstantArray[1, Length[vertices] {1, 1}]],
          
 VertexLabels -> Automatic
          
]


          enter image description here



          With IGraph/M, you can zero out the matrix diagonal directly:



          AdjacencyGraph[vertices, 
          
 IGZeroDiagonal@ConstantArray[1, Length[vertices] {1, 1}], 
          
 VertexLabels -> Automatic]





          share|improve this answer









          $endgroup$













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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            2












            $begingroup$

            Graph[UndirectedEdge @@@ Subsets[vertices, {2}], VertexLabels -> "Name"]


            enter image description here



            Alternatively, you can use any of the following to get the same result:



            SimpleGraph[RelationGraph[True &, vertices], VertexLabels -> "Name"]
            
AdjacencyGraph[vertices, ConstantArray[1, {5,5}]-IdentityMatrix[5], VertexLabels -> "Name"]
            
SetProperty[VertexReplace[#, Thread[VertexList@# -> vertices]] &@ CompleteGraph[5],
            
  VertexLabels -> "Name"]


            To change just the labels you can use:



            CompleteGraph[5, VertexLabels -> {k_ :> vertices[[k]]}]



            same picture







            share|improve this answer











            $endgroup$













            • $begingroup$
              The first CompleteGraph approach seems to only change the labels but not the vertex names. The other two versions work great, thank you! (True, I guess my question was asking about labels, sorry for the confusion.)
              $endgroup$
              – Kagaratsch
              10 hours ago












            • $begingroup$
              @Kagaratsch, my pleasure. Thank you for the accept.
              $endgroup$
              – kglr
              10 hours ago
















            2












            $begingroup$

            Graph[UndirectedEdge @@@ Subsets[vertices, {2}], VertexLabels -> "Name"]


            enter image description here



            Alternatively, you can use any of the following to get the same result:



            SimpleGraph[RelationGraph[True &, vertices], VertexLabels -> "Name"]
            
AdjacencyGraph[vertices, ConstantArray[1, {5,5}]-IdentityMatrix[5], VertexLabels -> "Name"]
            
SetProperty[VertexReplace[#, Thread[VertexList@# -> vertices]] &@ CompleteGraph[5],
            
  VertexLabels -> "Name"]


            To change just the labels you can use:



            CompleteGraph[5, VertexLabels -> {k_ :> vertices[[k]]}]



            same picture







            share|improve this answer











            $endgroup$













            • $begingroup$
              The first CompleteGraph approach seems to only change the labels but not the vertex names. The other two versions work great, thank you! (True, I guess my question was asking about labels, sorry for the confusion.)
              $endgroup$
              – Kagaratsch
              10 hours ago












            • $begingroup$
              @Kagaratsch, my pleasure. Thank you for the accept.
              $endgroup$
              – kglr
              10 hours ago














            2












            2








            2





            $begingroup$

            Graph[UndirectedEdge @@@ Subsets[vertices, {2}], VertexLabels -> "Name"]


            enter image description here



            Alternatively, you can use any of the following to get the same result:



            SimpleGraph[RelationGraph[True &, vertices], VertexLabels -> "Name"]
            
AdjacencyGraph[vertices, ConstantArray[1, {5,5}]-IdentityMatrix[5], VertexLabels -> "Name"]
            
SetProperty[VertexReplace[#, Thread[VertexList@# -> vertices]] &@ CompleteGraph[5],
            
  VertexLabels -> "Name"]


            To change just the labels you can use:



            CompleteGraph[5, VertexLabels -> {k_ :> vertices[[k]]}]



            same picture







            share|improve this answer











            $endgroup$



            Graph[UndirectedEdge @@@ Subsets[vertices, {2}], VertexLabels -> "Name"]


            enter image description here



            Alternatively, you can use any of the following to get the same result:



            SimpleGraph[RelationGraph[True &, vertices], VertexLabels -> "Name"]
            
AdjacencyGraph[vertices, ConstantArray[1, {5,5}]-IdentityMatrix[5], VertexLabels -> "Name"]
            
SetProperty[VertexReplace[#, Thread[VertexList@# -> vertices]] &@ CompleteGraph[5],
            
  VertexLabels -> "Name"]


            To change just the labels you can use:



            CompleteGraph[5, VertexLabels -> {k_ :> vertices[[k]]}]



            same picture








            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 9 hours ago

























            answered 10 hours ago









            kglrkglr

            179k9199410




            179k9199410












            • $begingroup$
              The first CompleteGraph approach seems to only change the labels but not the vertex names. The other two versions work great, thank you! (True, I guess my question was asking about labels, sorry for the confusion.)
              $endgroup$
              – Kagaratsch
              10 hours ago












            • $begingroup$
              @Kagaratsch, my pleasure. Thank you for the accept.
              $endgroup$
              – kglr
              10 hours ago


















            • $begingroup$
              The first CompleteGraph approach seems to only change the labels but not the vertex names. The other two versions work great, thank you! (True, I guess my question was asking about labels, sorry for the confusion.)
              $endgroup$
              – Kagaratsch
              10 hours ago












            • $begingroup$
              @Kagaratsch, my pleasure. Thank you for the accept.
              $endgroup$
              – kglr
              10 hours ago
















            $begingroup$
            The first CompleteGraph approach seems to only change the labels but not the vertex names. The other two versions work great, thank you! (True, I guess my question was asking about labels, sorry for the confusion.)
            $endgroup$
            – Kagaratsch
            10 hours ago






            $begingroup$
            The first CompleteGraph approach seems to only change the labels but not the vertex names. The other two versions work great, thank you! (True, I guess my question was asking about labels, sorry for the confusion.)
            $endgroup$
            – Kagaratsch
            10 hours ago














            $begingroup$
            @Kagaratsch, my pleasure. Thank you for the accept.
            $endgroup$
            – kglr
            10 hours ago




            $begingroup$
            @Kagaratsch, my pleasure. Thank you for the accept.
            $endgroup$
            – kglr
            10 hours ago











            1












            $begingroup$

            Another way is with AdjacencyGraph.



            SimpleGraph[
            
 AdjacencyGraph[vertices, ConstantArray[1, Length[vertices] {1, 1}]],
            
 VertexLabels -> Automatic
            
]


            enter image description here



            With IGraph/M, you can zero out the matrix diagonal directly:



            AdjacencyGraph[vertices, 
            
 IGZeroDiagonal@ConstantArray[1, Length[vertices] {1, 1}], 
            
 VertexLabels -> Automatic]





            share|improve this answer









            $endgroup$


















              1












              $begingroup$

              Another way is with AdjacencyGraph.



              SimpleGraph[
              
 AdjacencyGraph[vertices, ConstantArray[1, Length[vertices] {1, 1}]],
              
 VertexLabels -> Automatic
              
]


              enter image description here



              With IGraph/M, you can zero out the matrix diagonal directly:



              AdjacencyGraph[vertices, 
              
 IGZeroDiagonal@ConstantArray[1, Length[vertices] {1, 1}], 
              
 VertexLabels -> Automatic]





              share|improve this answer









              $endgroup$
















                1












                1








                1





                $begingroup$

                Another way is with AdjacencyGraph.



                SimpleGraph[
                
 AdjacencyGraph[vertices, ConstantArray[1, Length[vertices] {1, 1}]],
                
 VertexLabels -> Automatic
                
]


                enter image description here



                With IGraph/M, you can zero out the matrix diagonal directly:



                AdjacencyGraph[vertices, 
                
 IGZeroDiagonal@ConstantArray[1, Length[vertices] {1, 1}], 
                
 VertexLabels -> Automatic]





                share|improve this answer









                $endgroup$



                Another way is with AdjacencyGraph.



                SimpleGraph[
                
 AdjacencyGraph[vertices, ConstantArray[1, Length[vertices] {1, 1}]],
                
 VertexLabels -> Automatic
                
]


                enter image description here



                With IGraph/M, you can zero out the matrix diagonal directly:



                AdjacencyGraph[vertices, 
                
 IGZeroDiagonal@ConstantArray[1, Length[vertices] {1, 1}], 
                
 VertexLabels -> Automatic]






                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 8 hours ago









                SzabolcsSzabolcs

                159k13435930




                159k13435930






























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