Hypergraphs are trivial mathematical structures that can embed other data models. For instance, relations in relational models, and edges in graphs and tree data models can all be naturally represented by hyperedges. Hypergraphs into other data models are a non-trivial generalization where the translations may suffer information and semantic loss due to the richness of hypergraphs in representing complex data and complex relationships. The lossy translations may impact the representation of adequate information, as in hypergraphs. However, achieving a hypergraph-based lossless generalization is a challenge. To address this issue, this paper proposes an embedding-based hypergraph-mediated translation approach called Hypergraph Mediator or HgMed based on a high-level hypergraph data model. The HgMed involves translation patterns for schematic abstractions from hypergraphs to other models and vice versa, such that the repeated translations do not result in further loss of structural information. By providing a formal characterization, we propose a notion of translation correctness based on a simulation relation.

GraphQL, a query language, has gained industry adoption (including GitHub, Coursera, and Neo4j) due to its ability to specify structures for input data as objects at the application level and get query results for the required parts of the matched objects. Traditional GraphQL supports graphs and hierarchical structures. Its functionality can be enhanced by embracing the richness of hypergraphs so that the GraphQL can be employed with hypergraph databases. Hypergraphs are natural mathematical structures capable of representing data and complex relationships in different settings, such as hierarchical, navigational, relational, and semi-structured. In this paper, we propose and present Hypergraph-oriented GraphQL or HGQL that extends the GraphQL’s scope to embrace hypergraphs semantically and syntactically. We formalize the semantics of a class of schematic hypergraphs and queries in the HGQL. We also describe the syntactic details of our approach. Furthermore, we discuss how our proposed approach can be rendered in a hypergraph-oriented implementation.