There is a lot going on that isn't seen by the classical hierarchical structure. This is a great way to capture this.
I have been talking about doing a PageRank of sorts at work. To me, the interaction structure is a graph: credit can go both ways and between coworkers of the same unit. It could help a lot of the silent workers you only hear about when things go wrong.
Nothing concrete so far, but the thought experiment yielded some interest from colleagues. I wish it, or OP's back-propagation, could be implemented and tested.
What other use cases could this be applied to?
One I can conceptualize hazily would be manufacturing to lower defect rates or increase production rates, or something like that. I'm not sure what the structure would look like, or what the nodes would represent, but it feels like a plausible use case.
Perhaps it could also be applied to employee management (or other kinds of management)?
Part of the issue with other use cases is "getting the numbers"; it seems analogous to finding and applying metrics in various six sigma approaches - if you don't have an objective measure, you won't get very far. Now that I think a little bit about it, based on my limited knowledge and training in 6s, process mapping and optimization of processes was done in a kind of "backprop" manner...