What's the highest 'order' data structure Not sure exactly how to define this but here's the basis of the question (very loosely)


All lists can be contained in tree's
all trees can be contained in a graph
all graphs can be contained in a multi graph, 
and all multigraphs can be contained in a hypergraph (never actually heard of a hypergraph before searching for an answer to this, so may not have it quite right)


So there's a containment hierarchy of 'complexity' of data structures. Is Hypergraph the highest one, is there a proof of this, and is there a name for the study of whatever this is. 

By highest one, I mean all structures can be represented as a hypergraph if I chose to. So in any code I could represent all the structures by using a number of hypergraphs (not that I would). tia 

[Update] Perhaps an alternative way to ask it is, for any arrangement of data structures consisting of nodes and edges. Does there exist a structure that can't be contained in a hypergraph.

Then there is a second question - is there any data structure which can't be represented using nodes and edges.
Perhaps this is an interesting question with explicit answers, but you probably really have a problem with "exactly how to define this".

A list does not directly corresponds to a unique data structure, nor does a tree. A singly linked list corresponds to a (sufficiently unique) data structure, as does a binary tree. When you say multi graph, you probably want to refer to a quiver, i.e. a directed multigraph (edges with own identity). A binary or ternary quiver would again correspond to a (sufficiently unique) data structure.

However, any sufficiently canonical (and efficient) realization of a (n-ary) quiver as a data structure would probably not match well with the way datatypes are handled in "common" programming languages, where the size of an object with a certain datatype shouldn't depend on the actual content of that object. Therefore, this would be the point at which I would stop to look for a higher order data structure (than a quiver, looking for function like data structures and continuations certainly is useful). My reason for this is that I don't see the practical usefulness of a higher order data structure if it cannot be realized efficiently within "common" programming languages.