HIF: The hypergraph interchange format for higher-order networks

TL;DR

The paper addresses fragmentation in higher-order network data by introducing the Hypergraph Interchange Format (HIF), a JSON-based interchange standard that encodes both topology and rich incidence metadata for undirected, directed hypergraphs and abstract simplicial complexes. It provides a JSON schema, validation tools for Python, R, and Julia, and accompanying tutorials to facilitate cross-library interoperability. A case study demonstrates end-to-end interoperability across HAT, Hypergraphx, HyperNetX, SimpleHypergraphs.jl, and XGI on a publications hypergraph with $n=1960$ nodes and $m=533$ edges, illustrating how diverse analyses can be composed within a unified format. The work enables reproducible, cross-library workflows and points to future extensions to multiplex, temporal, and ordered hypergraphs, along with streaming formats like JSONL to address increasingly large datasets.

Abstract

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.

Figures (9)

• Figure 1: The JSON Schema is depicted as a graph, showing the hierarchy of properties for each data record. The example demonstrates the use of most properties including metadata for interpretability.
• Figure 2: Example code snippets for validating the schema in different languages. In all cases, url="https://raw.githubusercontent.com/pszufe/HIF-standard/main/schemas/hif_schema.json" and filepath is the local filepath of the file being validated.
• Figure 3: The example code demonstrates creating a HAT hypergraph from an example HIF JSON file and exporting it back to Python.
• Figure 4: Example demonstrating how to load a HIF-compliant file, use Hypergraphx (HGX) functionalities and export the file.
• Figure 5: Example demonstrating how to load and export and HIF file using HyperNetX (HNX).