dynamic - What is wrong with combining two programs with event handlers?

I can delete the unwanted nodes of a RandomGraph by double-clicking on them from the first program, and I can change the positions of the nodes by dragging them from the second program. They both work nicely. However, when I combined the two programs into one, the nodes can't be dragged anymore. What is wrong with the combined promgram? Please help.

(* First program, nodes can be deleted by double-clicking on them *)
DynamicModule[{rg },
 rg = RandomGraph[{7, 10}];
 edglst = EdgeList[rg];
 vlst = VertexList[rg];
 VPOS = VertexCoordinates /. AbsoluteOptions[rg, VertexCoordinates];

 VPOS = Rescale[#, 1 + Through[{Min, Max}[VPOS]], {0, 1}] & /@ VPOS;

 Vnthlrs = MapThread[EventHandler[#, {
      "MouseDown" :> If[CurrentValue["MouseClickCount"] == 2, ( 
         ep = First@Position[vlst, #];
         vlst = Drop[vlst, ep ];
         VPOS = Drop[VPOS, ep ];
         edglst = 
          Delete[edglst, Map[List, Position[edglst, #][[All, 1]]]];
         Vnthlrs = Drop[Vnthlrs, ep  ])]

      }] &, {vlst}];

  g = Dynamic@Graph[Vnthlrs, edglst,
    VertexCoordinates -> VPOS,
    VertexSize -> {.02, .02},
    VertexLabels -> "Name",
    PlotRange -> 1,
    EdgeStyle -> {Thick}
     ] 
  ]


(* Second program, nodes can be moved by dragging them *)
DynamicModule[{rg, refr = True},
 rg = RandomGraph[{7, 10}];
 edglst = EdgeList[rg];
 vlst = VertexList[rg];
 VPOS = VertexCoordinates /. AbsoluteOptions[rg, VertexCoordinates];
 VPOS = Rescale[#, 1 + Through[{Min, Max}[VPOS]], {0, 1}] & /@ VPOS;

 EventHandler[

  g = Dynamic@
    Graph[vlst, edglst, VertexCoordinates -> VPOS, 
     VertexSize -> {.02, .02},
     VertexLabels -> "Name",
     PlotRange -> 1,
     EdgeStyle -> {Thick}],
  {"MouseDown" :> (
      With[{pos = MousePosition["Graphics"]}, 
      ind = Position[VPOS, Nearest[VPOS, pos][[1]]][[1, 1]]]),


   "MouseDragged" :> 
    (VPOS[[ind ]] = MousePosition["Graphics"] )
     },
  PassEventsDown -> True
    ]
 ]

(* Combined *)
DynamicModule[{rg },
 rg = RandomGraph[{7, 10}];

 edglst = EdgeList[rg];
 vlst = VertexList[rg];
 VPOS = VertexCoordinates /. AbsoluteOptions[rg, VertexCoordinates];
 VPOS = Rescale[#, 1 + Through[{Min, Max}[VPOS]], {0, 1}] & /@ VPOS;

 Vnthlrs = MapThread[EventHandler[#, {
      "MouseDown" :> If[CurrentValue["MouseClickCount"] == 2, ( 
         ep = First@Position[vlst, #];
         vlst = Drop[vlst, ep ];
         VPOS = Drop[VPOS, ep ];

         edglst = 
          Delete[edglst, Map[List, Position[edglst, #][[All, 1]]]];
         Vnthlrs = Drop[Vnthlrs, ep  ])]
      }] &, {vlst}];

 EventHandler[
  g = Dynamic@
    Graph[Vnthlrs, edglst, VertexCoordinates -> VPOS, 
     VertexSize -> {.02, .02},
     VertexLabels -> "Name",

     PlotRange -> 1,
     EdgeStyle -> {Thick}],
  {"MouseDown" :> (
      With[{pos = MousePosition["Graphics"]}, 
      ind = Position[VPOS, Nearest[VPOS, pos][[1]]][[1, 1]]]),

   "MouseDragged" :> 
    (VPOS[[ind ]] = MousePosition["Graphics"] )
     },
  PassEventsDown -> True

  ]
 ]

Answer

Finally, I discovered that the combined program works fine as long as the dragging just begin from the point close to the node (not right on the top of it). Thanks.