HIF: The hypergraph interchange format for higher-order networks

Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order interactions and the collection of these interactions comprise a higher-order network, or hypergraph. Hypergraphs have established themselves as a popular and versatile mathematical representation of such systems and a number of software packages written in various programming languages have been designed to analyze these networks. However, the ecosystem of higher-order network analysis software is fragmented due to specialization of each software’s programming interface and compatible data representations. To enable seamless data exchange between higher-order network analysis software packages, we introduce the Hypergraph Interchange Format (HIF), a standardized format for storing higher-order network data. HIF supports multiple types of higher-order networks, including undirected hypergraphs, directed hypergraphs, and abstract simplicial complexes, while actively exploring extensions to represent multiplex hypergraphs, temporal hypergraphs, and ordered hypergraphs. To accommodate the wide variety of metadata used in different contexts, HIF also includes support for attributes associated with nodes, edges, and incidences. This initiative is a collaborative effort involving authors, maintainers, and contributors from prominent hypergraph software packages. This project introduces a JSON schema with corresponding documentation and unit tests, example HIF-compliant datasets, and tutorials demonstrating the use of HIF with several popular higher-order network analysis software packages.

💡 Research Summary

The paper addresses a critical gap in the emerging field of higher‑order network science: the lack of a unified data interchange format for hypergraphs and related structures. While traditional graph formats such as GraphML, GEXF, or Pajek efficiently encode pairwise (dyadic) relationships, they fall short when interactions involve three or more entities, a situation common in co‑authorship networks, chemical reaction systems, social group dynamics, and ecological dependencies. Existing hypergraph libraries—XGI, HypergraphR, Hypergraphx, among others—each define their own proprietary serialization schemes, leading to duplicated datasets, fragmented repositories, and a high overhead for researchers who must write custom conversion scripts for every new tool in their workflow.

To resolve this fragmentation, the authors introduce the Hypergraph Interchange Format (HIF), a JSON‑based schema designed to be language‑agnostic, human‑readable, and extensible. The top‑level object contains a network-type field (accepting values such as “undirected”, “directed”, or “simplicial”) and a metadata block for bibliographic information (title, collection date, DOI, etc.). The core of the format is divided into three sections: nodes, hyperedges, and incidences. Each node and hyperedge can carry an arbitrary dictionary of attributes, enabling the storage of domain‑specific information (e.g., geographic coordinates for nodes, reaction rates for hyperedges). Crucially, HIF also supports attributes on incidences—the (node, hyperedge) pairs—allowing the explicit encoding of tail/head membership in directed hyperedges, edge‑dependent weights, or any other per‑incidence property. This design choice directly mirrors the mathematical definition of a hypergraph as a triple (H = (V, E, I)) where (I \subseteq V \times E) is the incidence relation, and it accommodates multihypergraphs (duplicate hyperedges) as well as degenerate cases such as empty hyperedges or self‑loops.

The schema is deliberately extensible. An extensions field is reserved for future capabilities, currently described as “actively exploring” support for multiplex hypergraphs (multiple layers of interactions), temporal hypergraphs (time‑stamped incidences), and ordered hypergraphs (where the order of vertices within a hyperedge matters). By providing a clear path for extension, HIF aims to remain relevant as higher‑order network theory evolves.

Implementation details are thoroughly documented. The authors supply a JSON Schema file that can be validated with standard libraries in Python, R, and Julia, and they provide unit tests that are integrated into the continuous‑integration pipelines of the participating libraries. Example datasets spanning social, chemical, and biological domains are released in HIF format, accompanied by step‑by‑step tutorials that demonstrate loading, converting, and visualizing data across XGI (Python), Hypergraphx (Julia), and HypergraphR (C++). These examples illustrate how a researcher can construct a hypergraph in one environment, export it as HIF, and seamlessly import it into another without loss of topology or attribute information.

The authors acknowledge several limitations. JSON, while excellent for readability and cross‑language support, can become bulky for massive hypergraphs containing millions of hyperedges; the paper suggests optional gzip compression or future integration with columnar binary formats such as Apache Parquet for large‑scale applications. Additionally, the governance model for schema evolution is outlined but not fully fleshed out; the authors propose a community‑driven process, possibly involving a steering committee, to manage versioning and to incorporate feedback from a broader user base.

In the discussion, the paper positions HIF alongside successful standards in adjacent fields, such as ONNX for machine‑learning model exchange and GraphML for traditional graph data. By providing a common lingua franca, HIF is expected to improve reproducibility, lower the barrier to entry for new researchers, and foster collaborative development of higher‑order network algorithms. The authors conclude that widespread adoption of HIF could accelerate the maturation of hypergraph science, enabling more robust cross‑disciplinary studies and facilitating the integration of hypergraph analytics into mainstream data‑science pipelines.