The hyper volumes between vertices can have single weights. Say you have a pump that is contaminated with cholera. You can either model the pump as a node on the graph with every person drinking from it being connected by an edge, allow an arbitrary number of edges between any two nodes, or allow for a relationship that can connect an arbitrary number of nodes.
I built a rather sophisticated simplex based trade analyser for one of my contracts for a broker trader. From what I've heard it's given them an edge since no one even knows about it. It's been three years so my NDA and non-compete are finished. I might get around to writing it up if I don't get hired to do another one.
With hypervolumes you mean all the (n-1)-dimensional 'faces' (n > 1) formed by a vertex and its neighbours in an n-dimensional simplex or a mesh of those? To assign unique weights to all interactions between a vertex and up to n-1 of its neighbours, I assume.
I built a rather sophisticated simplex based trade analyser for one of my contracts for a broker trader. From what I've heard it's given them an edge since no one even knows about it. It's been three years so my NDA and non-compete are finished. I might get around to writing it up if I don't get hired to do another one.