# 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.

• I don't know how clearly defined this question is. I can imagine that for any structure you come up with, I can create a higher order one. Sep 27, 2012 at 10:46
• how so? I can't think of any thing that I'd need more than a multi graph for, e.g. 3d space and so on. If I need a multigraph of multigraphs then that is a multigraph as well (in the most abstract relationship sense) Sep 27, 2012 at 10:49
• I could probably add edges between nodes and edges at one level. Then I could add edges between edges (of the lower level). Then for each new level, I could add new kinds of edges that go between edges of the lower level .... Sep 27, 2012 at 10:53
• I cannot connect edges with edges in a multigraph. Sep 27, 2012 at 11:00
• Don't think you can have a "directed" hypergraph, since it's just a family of sets. Hence: "Does there exist a structure that can't be contained in a hypergraph." ... any directed graph. Sep 27, 2012 at 11:41