Select connected subsets of integer pairs?

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Given a list of integer pairs such as



list = 1,2,1,3,2,5,1,5,6,7,6,9,4,6 ;


What is a quick way to separate the pairs into groups in which every element shares at least one integer with at least one other element, in Mathematica? e.g.:



separate[list]



1,2,1,3,2,5,1,5 , 6,7,6,9,4,6




Thanks for any suggestion!






list-manipulation function-construction







share|improve this question

























    up vote
    5
    down vote

    favorite
    1












    Given a list of integer pairs such as



    list = 1,2,1,3,2,5,1,5,6,7,6,9,4,6 ;


    What is a quick way to separate the pairs into groups in which every element shares at least one integer with at least one other element, in Mathematica? e.g.:



    separate[list]



    1,2,1,3,2,5,1,5 , 6,7,6,9,4,6




    Thanks for any suggestion!






    list-manipulation function-construction







    share|improve this question























      up vote
      5
      down vote

      favorite
      1









      up vote
      5
      down vote

      favorite
      1






      1





      Given a list of integer pairs such as



      list = 1,2,1,3,2,5,1,5,6,7,6,9,4,6 ;


      What is a quick way to separate the pairs into groups in which every element shares at least one integer with at least one other element, in Mathematica? e.g.:



      separate[list]



      1,2,1,3,2,5,1,5 , 6,7,6,9,4,6




      Thanks for any suggestion!






      list-manipulation function-construction







      share|improve this question













      Given a list of integer pairs such as



      list = 1,2,1,3,2,5,1,5,6,7,6,9,4,6 ;


      What is a quick way to separate the pairs into groups in which every element shares at least one integer with at least one other element, in Mathematica? e.g.:



      separate[list]



      1,2,1,3,2,5,1,5 , 6,7,6,9,4,6




      Thanks for any suggestion!






      list-manipulation function-construction




      list-manipulation function-construction






      share|improve this question













      share|improve this question











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      share|improve this question










      asked 4 hours ago









      Kagaratsch

      4,49131246




      4,49131246




















          2 Answers
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          G = Graph[1, 2, 1, 3, 2, 5, 1, 5, 6, 7, 6, 9, 4, 6];
          Select[
           List @@@ EdgeList[Subgraph[G, #]] & /@ ConnectedComponents[G], 
           Length[#]>0 &
           ]



          4, 6, 6, 7, 6, 9, 1, 2, 1, 3, 2, 5, 1, 5







          share|improve this answer





























            up vote
            1
            down vote













            Gather[list, IntersectingQ]



            1, 2, 1, 3, 2, 5, 1, 5,

            6, 7, 6, 9, 4, 6







            share|improve this answer




















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              2 Answers
              2






              active

              oldest

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              2 Answers
              2






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              active

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              up vote
              4
              down vote



              accepted










              G = Graph[1, 2, 1, 3, 2, 5, 1, 5, 6, 7, 6, 9, 4, 6];
              Select[
               List @@@ EdgeList[Subgraph[G, #]] & /@ ConnectedComponents[G], 
               Length[#]>0 &
               ]



              4, 6, 6, 7, 6, 9, 1, 2, 1, 3, 2, 5, 1, 5







              share|improve this answer


























                up vote
                4
                down vote



                accepted










                G = Graph[1, 2, 1, 3, 2, 5, 1, 5, 6, 7, 6, 9, 4, 6];
                Select[
                 List @@@ EdgeList[Subgraph[G, #]] & /@ ConnectedComponents[G], 
                 Length[#]>0 &
                 ]



                4, 6, 6, 7, 6, 9, 1, 2, 1, 3, 2, 5, 1, 5







                share|improve this answer
























                  up vote
                  4
                  down vote



                  accepted







                  up vote
                  4
                  down vote



                  accepted






                  G = Graph[1, 2, 1, 3, 2, 5, 1, 5, 6, 7, 6, 9, 4, 6];
                  Select[
                   List @@@ EdgeList[Subgraph[G, #]] & /@ ConnectedComponents[G], 
                   Length[#]>0 &
                   ]



                  4, 6, 6, 7, 6, 9, 1, 2, 1, 3, 2, 5, 1, 5







                  share|improve this answer














                  G = Graph[1, 2, 1, 3, 2, 5, 1, 5, 6, 7, 6, 9, 4, 6];
                  Select[
                   List @@@ EdgeList[Subgraph[G, #]] & /@ ConnectedComponents[G], 
                   Length[#]>0 &
                   ]



                  4, 6, 6, 7, 6, 9, 1, 2, 1, 3, 2, 5, 1, 5








                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 4 hours ago

























                  answered 4 hours ago









                  Henrik Schumacher

                  44k263129




                  44k263129




















                      up vote
                      1
                      down vote













                      Gather[list, IntersectingQ]



                      1, 2, 1, 3, 2, 5, 1, 5,

                      6, 7, 6, 9, 4, 6







                      share|improve this answer
























                        up vote
                        1
                        down vote













                        Gather[list, IntersectingQ]



                        1, 2, 1, 3, 2, 5, 1, 5,

                        6, 7, 6, 9, 4, 6







                        share|improve this answer






















                          up vote
                          1
                          down vote










                          up vote
                          1
                          down vote









                          Gather[list, IntersectingQ]



                          1, 2, 1, 3, 2, 5, 1, 5,

                          6, 7, 6, 9, 4, 6







                          share|improve this answer












                          Gather[list, IntersectingQ]



                          1, 2, 1, 3, 2, 5, 1, 5,

                          6, 7, 6, 9, 4, 6








                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered 12 mins ago









                          kglr

                          169k8193396




                          169k8193396



























                               

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