HyMeKo Language : Describing Complex Hypergraph-Like Data

Abstract

Numerous applications of computer science — including artificial intelligence, robotics, and cyber-physical systems — rely on highly connected data structures. Such complex information is most naturally and compactly described using a hypergraph-based approach, which enables concise representation of many-to-many relationships. In this paper, we introduce HyMeKo, a formal markup language designed to represent highly connected data based on hypergraph theory. Unlike traditional formats such as XML or JSON, HyMeKo offers a significantly more concise and semantically expressive way to model complex relationships by organizing data into a hypertree-based structure. The language supports template-based modeling and inheritance, enabling reusable, modular, and scalable data descriptions. HyMeKo is implemented as an LALR(1)-compliant language, allowing efficient parsing and transformation of structured data into hypergraphs. We provide a formal definition of the language, its supported operations, and relational rules, along with a comparative analysis demonstrating its syntactic efficiency. Application examples include robotic system descriptions, neural network architectures, and structured LLM prompts. We further present a structural complexity analysis showing that HyMeKo achieves a (k+1)-fold reduction in representational overhead compared to RDF reification for k-ary relationships, and provide an explicit comparison with RDF, OWL, and GraphQL. Reference implementations exist in both Python (PyLark) and Rust (LALRPOP). © 2026, Budapest Tech Polytechnical Institution. All rights reserved.