What are the rudimentary types of information connectivity i.e. model types?
Model theory, branch of mathematical logic, is based on three things: atoms, functions, and relations. With these you can define pretty much anything. In fact, functions are subsumed by relations, so you only need two.

What is a list but a next relation? What is a hierarchy but a parent-child relation?

Of course these satisfy axioms, and these can readily be expressed in first order logic.