Hi Danny, also I guess just a shortcut for doing a regular invert would do the trick as well. 
 
It's pretty handy to have that set up on the I key. To do that, go to Options > Shortcut keys and add in a new one. 
 
For the key put in I and for the command part put in this: 
script:moi.geometryDatabase.invertSelection(); 
 
After that you can invert the selection anytime by pushing the I key. 
 
Then to use it with the scene browser, do one right-click on the selection dot for the item - that will make that item the isolated selection deselecting any other things. Then push I after that and you should get your inverted selection that you want. 
 
The only thing to be aware of is that if you have sub-objects selected (faces or edges), it will invert the selection of the same kind of sub-objects within that same parent and not alter other things. 
 
    - Michael 
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