Question: Remove plot structure

This question is related to the Question Arrowed labels in graph

There is a cool option of dropping one graph from multigraph (after that it goes as separated one). How to get  this dropped structure itself? I.e. i have "graph" component with command AllPlots that itself is

AllPlots:=plots[display](AllPlotsStructure,...);

AllPlotsStructure is a list of plot/textplot.

After all i removed one structure by drag-and-drop on component. How to update AllPlotsStructure correctly?

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