Ok. I don't know the word simplex, but after brief googling, it looks like simplexes are a type of network.

Could you explain what you mean a little bit more?

Why are they simplexes? I'm reading about simplexes, and having a hard time visualizing how they map to social networks

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.

Yeah. And because they are sparse the representation is both tiny and stupidly powerful.

Would you care to share some pointers to materials where one could learn about simplicial representations of things traditionally modeled by networks?

There aren't any I could find, I had to do everything from first principles and the notebooks were left with my employer.

Maybe you mean something like a simplicial complex? I don't understand how you can do very much with a single simplex (which is a generalization of a triangle and a tetrahedron in the language I'm used to).

I think he is talking about a simplex tree.

Your comment informs little.

Do you mean that real social networks are to networks as tensors are to vectors? More dimensions?

If so, what do those dimensions represent?

Or am I missing your point (which is ... not very clearly made).