How to remove vertices from a graph?












2














I have 2 lists: list 1 is a list of vertices of a graph, says, {1,2,3,4,5} and list 2 keeps track of edges (i.e which vertex connects to which) such as {{1,2}, {2,3},{3,4},{4,1},{2,5}}. Now I want to remove some vertices in list 1 and I want that any edges in list 2 that have an end same as one of the removed vertices will also be removed. What would be the best way to do this in Mathematica? (I can do this easily in other languages like vb.net, but I still am trying to get my head on Mathematica)






list-manipulation graphs-and-networks







share|improve this question





























    2














    I have 2 lists: list 1 is a list of vertices of a graph, says, {1,2,3,4,5} and list 2 keeps track of edges (i.e which vertex connects to which) such as {{1,2}, {2,3},{3,4},{4,1},{2,5}}. Now I want to remove some vertices in list 1 and I want that any edges in list 2 that have an end same as one of the removed vertices will also be removed. What would be the best way to do this in Mathematica? (I can do this easily in other languages like vb.net, but I still am trying to get my head on Mathematica)






    list-manipulation graphs-and-networks







    share|improve this question



























      2












      2








      2


      1





      I have 2 lists: list 1 is a list of vertices of a graph, says, {1,2,3,4,5} and list 2 keeps track of edges (i.e which vertex connects to which) such as {{1,2}, {2,3},{3,4},{4,1},{2,5}}. Now I want to remove some vertices in list 1 and I want that any edges in list 2 that have an end same as one of the removed vertices will also be removed. What would be the best way to do this in Mathematica? (I can do this easily in other languages like vb.net, but I still am trying to get my head on Mathematica)






      list-manipulation graphs-and-networks







      share|improve this question















      I have 2 lists: list 1 is a list of vertices of a graph, says, {1,2,3,4,5} and list 2 keeps track of edges (i.e which vertex connects to which) such as {{1,2}, {2,3},{3,4},{4,1},{2,5}}. Now I want to remove some vertices in list 1 and I want that any edges in list 2 that have an end same as one of the removed vertices will also be removed. What would be the best way to do this in Mathematica? (I can do this easily in other languages like vb.net, but I still am trying to get my head on Mathematica)






      list-manipulation graphs-and-networks




      list-manipulation graphs-and-networks






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 50 mins ago









      Henrik Schumacher

      48.8k467139




      48.8k467139










      asked 2 hours ago









      N.T.C

      28517




      28517






















          4 Answers
          4






          active

          oldest

          votes


















          3














          These are done easily with graph functions:



          g = Graph[Range[5], {1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 1, 2 <-> 5}];


          enter image description here



          g2 = VertexDelete[g, 1];


          enter image description here



          EdgeList[g2]


          (*



          {2 <-> 3, 3 <-> 4, 2 <-> 5}



          *)



          Of course this works as well if you want to delete more than one vertex, e.g., vertices 1 and 5:



          g2 = VertexDelete[g, {1, 5}];





          share|improve this answer































            1














            edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};


            A few more alternatives:



            Select[edges, FreeQ[1]]
            
Pick[edges, FreeQ[1] /@ edges]
            
DeleteCases[edges, {_, 1} | {1, _}]
            
List @@@ EdgeList[VertexDelete[edges, 1]]


            all give




            {{2, 3}, {3, 4}, {2, 5}}







            share|improve this answer





















            • Your first three suggestions only work for removing a single vertex.
              – geordie
              1 hour ago






            • 1




              @geordie, if you want to remove a list of vertices, say {1,2}, you can use 1|2 instead of 1.
              – kglr
              1 hour ago





















            1














            The following works for removing several vertices and corresponding edges:



            verts = {1, 2, 3, 4, 5};
            
edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};
            

            
vertdel = {1, 4}
            
verts2 = Complement[verts, vertdel]
            
edges2 = Complement[edges, Flatten[Select[edges, MemberQ[#]] & /@ vertdel, 1]]



            {1, 4}



            {2, 3, 5}



            {{2, 3}, {2, 5}}







            share|improve this answer





























              0














              Tiny keyboard alert. 



              A = SparseArray[edges -> 1, {1 ,1} Max[edges]];
              
a = DiagonalMatrix[SparseArray[vertdel -> 0, {Length[A]}, 1]];
              
(a.A.a)["NonzeroPositions"]





              share|improve this answer























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                4 Answers
                4






                active

                oldest

                votes








                4 Answers
                4






                active

                oldest

                votes









                active

                oldest

                votes






                active

                oldest

                votes









                3














                These are done easily with graph functions:



                g = Graph[Range[5], {1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 1, 2 <-> 5}];


                enter image description here



                g2 = VertexDelete[g, 1];


                enter image description here



                EdgeList[g2]


                (*



                {2 <-> 3, 3 <-> 4, 2 <-> 5}



                *)



                Of course this works as well if you want to delete more than one vertex, e.g., vertices 1 and 5:



                g2 = VertexDelete[g, {1, 5}];





                share|improve this answer




























                  3














                  These are done easily with graph functions:



                  g = Graph[Range[5], {1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 1, 2 <-> 5}];


                  enter image description here



                  g2 = VertexDelete[g, 1];


                  enter image description here



                  EdgeList[g2]


                  (*



                  {2 <-> 3, 3 <-> 4, 2 <-> 5}



                  *)



                  Of course this works as well if you want to delete more than one vertex, e.g., vertices 1 and 5:



                  g2 = VertexDelete[g, {1, 5}];





                  share|improve this answer


























                    3












                    3








                    3






                    These are done easily with graph functions:



                    g = Graph[Range[5], {1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 1, 2 <-> 5}];


                    enter image description here



                    g2 = VertexDelete[g, 1];


                    enter image description here



                    EdgeList[g2]


                    (*



                    {2 <-> 3, 3 <-> 4, 2 <-> 5}



                    *)



                    Of course this works as well if you want to delete more than one vertex, e.g., vertices 1 and 5:



                    g2 = VertexDelete[g, {1, 5}];





                    share|improve this answer














                    These are done easily with graph functions:



                    g = Graph[Range[5], {1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 1, 2 <-> 5}];


                    enter image description here



                    g2 = VertexDelete[g, 1];


                    enter image description here



                    EdgeList[g2]


                    (*



                    {2 <-> 3, 3 <-> 4, 2 <-> 5}



                    *)



                    Of course this works as well if you want to delete more than one vertex, e.g., vertices 1 and 5:



                    g2 = VertexDelete[g, {1, 5}];






                    share|improve this answer














                    share|improve this answer



                    share|improve this answer








                    edited 1 hour ago

























                    answered 1 hour ago









                    David G. Stork

                    23.1k22051




                    23.1k22051























                        1














                        edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};


                        A few more alternatives:



                        Select[edges, FreeQ[1]]
                        
Pick[edges, FreeQ[1] /@ edges]
                        
DeleteCases[edges, {_, 1} | {1, _}]
                        
List @@@ EdgeList[VertexDelete[edges, 1]]


                        all give




                        {{2, 3}, {3, 4}, {2, 5}}







                        share|improve this answer





















                        • Your first three suggestions only work for removing a single vertex.
                          – geordie
                          1 hour ago






                        • 1




                          @geordie, if you want to remove a list of vertices, say {1,2}, you can use 1|2 instead of 1.
                          – kglr
                          1 hour ago


















                        1














                        edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};


                        A few more alternatives:



                        Select[edges, FreeQ[1]]
                        
Pick[edges, FreeQ[1] /@ edges]
                        
DeleteCases[edges, {_, 1} | {1, _}]
                        
List @@@ EdgeList[VertexDelete[edges, 1]]


                        all give




                        {{2, 3}, {3, 4}, {2, 5}}







                        share|improve this answer





















                        • Your first three suggestions only work for removing a single vertex.
                          – geordie
                          1 hour ago






                        • 1




                          @geordie, if you want to remove a list of vertices, say {1,2}, you can use 1|2 instead of 1.
                          – kglr
                          1 hour ago
















                        1












                        1








                        1






                        edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};


                        A few more alternatives:



                        Select[edges, FreeQ[1]]
                        
Pick[edges, FreeQ[1] /@ edges]
                        
DeleteCases[edges, {_, 1} | {1, _}]
                        
List @@@ EdgeList[VertexDelete[edges, 1]]


                        all give




                        {{2, 3}, {3, 4}, {2, 5}}







                        share|improve this answer












                        edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};


                        A few more alternatives:



                        Select[edges, FreeQ[1]]
                        
Pick[edges, FreeQ[1] /@ edges]
                        
DeleteCases[edges, {_, 1} | {1, _}]
                        
List @@@ EdgeList[VertexDelete[edges, 1]]


                        all give




                        {{2, 3}, {3, 4}, {2, 5}}








                        share|improve this answer












                        share|improve this answer



                        share|improve this answer










                        answered 1 hour ago









                        kglr

                        176k9198404




                        176k9198404












                        • Your first three suggestions only work for removing a single vertex.
                          – geordie
                          1 hour ago






                        • 1




                          @geordie, if you want to remove a list of vertices, say {1,2}, you can use 1|2 instead of 1.
                          – kglr
                          1 hour ago




















                        • Your first three suggestions only work for removing a single vertex.
                          – geordie
                          1 hour ago






                        • 1




                          @geordie, if you want to remove a list of vertices, say {1,2}, you can use 1|2 instead of 1.
                          – kglr
                          1 hour ago


















                        Your first three suggestions only work for removing a single vertex.
                        – geordie
                        1 hour ago




                        Your first three suggestions only work for removing a single vertex.
                        – geordie
                        1 hour ago




                        1




                        1




                        @geordie, if you want to remove a list of vertices, say {1,2}, you can use 1|2 instead of 1.
                        – kglr
                        1 hour ago






                        @geordie, if you want to remove a list of vertices, say {1,2}, you can use 1|2 instead of 1.
                        – kglr
                        1 hour ago













                        1














                        The following works for removing several vertices and corresponding edges:



                        verts = {1, 2, 3, 4, 5};
                        
edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};
                        

                        
vertdel = {1, 4}
                        
verts2 = Complement[verts, vertdel]
                        
edges2 = Complement[edges, Flatten[Select[edges, MemberQ[#]] & /@ vertdel, 1]]



                        {1, 4}



                        {2, 3, 5}



                        {{2, 3}, {2, 5}}







                        share|improve this answer


























                          1














                          The following works for removing several vertices and corresponding edges:



                          verts = {1, 2, 3, 4, 5};
                          
edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};
                          

                          
vertdel = {1, 4}
                          
verts2 = Complement[verts, vertdel]
                          
edges2 = Complement[edges, Flatten[Select[edges, MemberQ[#]] & /@ vertdel, 1]]



                          {1, 4}



                          {2, 3, 5}



                          {{2, 3}, {2, 5}}







                          share|improve this answer
























                            1












                            1








                            1






                            The following works for removing several vertices and corresponding edges:



                            verts = {1, 2, 3, 4, 5};
                            
edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};
                            

                            
vertdel = {1, 4}
                            
verts2 = Complement[verts, vertdel]
                            
edges2 = Complement[edges, Flatten[Select[edges, MemberQ[#]] & /@ vertdel, 1]]



                            {1, 4}



                            {2, 3, 5}



                            {{2, 3}, {2, 5}}







                            share|improve this answer












                            The following works for removing several vertices and corresponding edges:



                            verts = {1, 2, 3, 4, 5};
                            
edges = {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {2, 5}};
                            

                            
vertdel = {1, 4}
                            
verts2 = Complement[verts, vertdel]
                            
edges2 = Complement[edges, Flatten[Select[edges, MemberQ[#]] & /@ vertdel, 1]]



                            {1, 4}



                            {2, 3, 5}



                            {{2, 3}, {2, 5}}








                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered 1 hour ago









                            geordie

                            1,9781530




                            1,9781530























                                0














                                Tiny keyboard alert. 



                                A = SparseArray[edges -> 1, {1 ,1} Max[edges]];
                                
a = DiagonalMatrix[SparseArray[vertdel -> 0, {Length[A]}, 1]];
                                
(a.A.a)["NonzeroPositions"]





                                share|improve this answer




























                                  0














                                  Tiny keyboard alert. 



                                  A = SparseArray[edges -> 1, {1 ,1} Max[edges]];
                                  
a = DiagonalMatrix[SparseArray[vertdel -> 0, {Length[A]}, 1]];
                                  
(a.A.a)["NonzeroPositions"]





                                  share|improve this answer


























                                    0












                                    0








                                    0






                                    Tiny keyboard alert. 



                                    A = SparseArray[edges -> 1, {1 ,1} Max[edges]];
                                    
a = DiagonalMatrix[SparseArray[vertdel -> 0, {Length[A]}, 1]];
                                    
(a.A.a)["NonzeroPositions"]





                                    share|improve this answer














                                    Tiny keyboard alert. 



                                    A = SparseArray[edges -> 1, {1 ,1} Max[edges]];
                                    
a = DiagonalMatrix[SparseArray[vertdel -> 0, {Length[A]}, 1]];
                                    
(a.A.a)["NonzeroPositions"]






                                    share|improve this answer














                                    share|improve this answer



                                    share|improve this answer








                                    edited 28 mins ago

























                                    answered 43 mins ago









                                    Henrik Schumacher

                                    48.8k467139




                                    48.8k467139






























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