You can set Visible property to [u]mode.equals("edit_v-t_graph")[/u] if you want it to be drawn on the condition that mode.equals("edit_v-t_graph") is true.

You can only drag an object when it is visible. (Unless you draw the object the same color as the background-- the object was draw but user might not be able to see it. this is different case)

Is this what you want?