(Disclaimer: I am not a mathematician)

A not well-defined set A contains itself:

  A <element_of> A

How to name a not well-defined set's property of containing itself via a nesting structure in other sets?

  A <element_of> B <element_of> A
  A <element_of> B <element_of> C <element_of> A

In hypergraphs, hyperedges can link multiple vertices. Metagraphs extend hypergraphs in that hyperedges can link multiple other hyperedges, as well as vertices. I have been unable to find a universally accepted definition of the concept of metagraphs.

  [hypergraph] hyperedge E links vertices A, B, and C
  [metagraph] hyperedge E links vertices A, B, and C; hyperedge F links vertices A and B with hyperedge E

How to call a metagraph with self-containment cycles whereby a hyperedge E points to itself via another hyperedge F?

  [nested cyclic metagraph?] hyperedge E links hyperedge F with vertices B and C; hyperedge F links vertices A and B with hyperedge E

A similar nesting parallel may be drawn with n-categories.

Finding literature on such data structures may become easier with a commonly accepted name, but the latter has eluded me for years. Should you have any ideas or pointers, please, put them down here.