Hypergraph Interchange Format (HIF)

Updated 19 July 2025

Hypergraph Interchange Format (HIF) is a standardized, JSON-based specification for representing complex higher-order networks with flexible metadata annotations.
It supports undirected, directed, and simplicial-complex structures that facilitate reproducible research and seamless interoperability across diverse analytical platforms.
Its extensible schema and community-driven development enable advanced data modeling in fields such as coauthorship networks, ecological webs, and chemical reaction systems.

The Hypergraph Interchange Format (HIF) is a standardized, schema-driven specification for representing higher-order network data. Designed around a flexible JSON encoding, HIF enables the exchange, storage, and joint analysis of hypergraphs, directed hypergraphs, and simplicial complexes between diverse software platforms and research domains. Its development is driven by the need to unify data representations across a fragmented higher-order network science ecosystem, supporting reproducible research and enabling rich metadata annotation and extensibility across emerging network types (Coll et al., 15 Jul 2025).

1. Definition and Scope of HIF

HIF is a unified interchange format tailored for datasets whose fundamental interactions go beyond simple pairwise (dyadic) relationships, commonly encountered in empirical systems such as chemical reaction networks, coauthorship, ecological food webs, and group social interactions. In HIF, a “higher-order network” is one where interactions (hyperedges or simplices) may involve an arbitrary number of entities (nodes), frequently reflecting a more faithful encoding of the observed phenomena than traditional graphs (Coll et al., 15 Jul 2025).

The HIF specification incorporates:

Undirected hypergraphs: Each hyperedge is a set of nodes.
Directed hypergraphs: Each incidence has an associated direction (e.g., ‘head’ or ‘tail’).
Simplicial complexes: Downward-closed hypergraph structures, with specific guidelines for storing maximal simplices and select subfaces.

Actively explored extensions include multiplex hypergraphs (multiple layers), temporal hypergraphs (time-tagged interactions), and ordered hypergraphs (with significant node ordering in hyperedges) (Coll et al., 15 Jul 2025).

2. Structural Features and Core Schema

HIF’s foundation is a rigorously defined JSON schema that specifies both structural components and allowed metadata. The primary schema entities are:

"network-type": Enumerated as "undirected", "directed", or "simplicial-complex"; defines the mathematical model used.
"metadata": Captures global dataset-level annotations (e.g., name, dataset version, collection context, references).
"nodes": Array of node descriptors, each possibly including arbitrary attributes (e.g., role, tag, auxiliary labels).
"edges": Array of edge (hyperedge or simplex) descriptors, each likewise supporting attribute maps (e.g., edge weights, semantic types, data provenance).
"incidences": List of node–hyperedge relationships; for directed hypergraphs, incidences include directionality (“head” or “tail”), and may support per-incidence attributes such as weight or context-specific roles.

A minimal HIF example for a directed hypergraph:

{
  "network-type": "directed",
  "metadata": { "name": "Example Hypergraph Dataset", "source": "ArXiv", "date": "2025-07" },
  "nodes": [{ "node": 1, "attrs": {"role": "author"} }],
  "edges": [{ "edge": 10, "attrs": {"publication": "Sample Paper"} }],
  "incidences": [
    { "edge": 10, "node": 1, "weight": 2, "direction": "tail", "attrs": {"role": "PI"} }
  ]
}

This design supports both minimal and richly annotated higher-order networks, enabling flexible mapping from and to many scientific datasets (Coll et al., 15 Jul 2025).

3. Metadata, Attributes, and Extensibility

Support for metadata at multiple levels is central to HIF. Attributes can be attached to the network as a whole, individual nodes, hyperedges (or simplices), and even specific incidences (node–edge pairs).

Network-level metadata assists with data provenance, citation, and contextualization.
Node and edge attributes allow detailed annotation (examples: node type, group membership, edge capacity, experimental condition).
Incidence metadata enables modeling of directedness, role designation (e.g., “PI” in authorship), and quantitative weights critical for random walk and influence processes.

The schema accommodates optional or library-specific attributes, allowing individual research groups or software packages to encode auxiliary data as needed without breaking interoperability (Coll et al., 15 Jul 2025).

The format is designed for extensibility. Although HIF currently supports undirected, directed, and simplicial complex representations, developers are extending it to cover multiplex, temporal, partially ordered, and ordered hypergraphs. The schema is maintained under semantic versioning and includes a publicly available changelog to track new features (Coll et al., 15 Jul 2025).

4. Community-Driven Development and Technical Infrastructure

HIF is a collaborative initiative involving contributors from major higher-order network software packages such as HyperNetX, XGI, Hypergraphx (HGX), SimpleHypergraphs.jl, and the Hypergraph Analysis Toolbox (HAT). This collaborative model ensures the specification responds to practical analysis requirements encountered across scientific disciplines.

Technical highlights include:

A well-documented JSON schema.
Unit tests for schema validation.
Sample datasets exemplifying correct HIF usage.
Tutorials demonstrating loading, analysis, and transformation of HIF data in multiple programming environments (Python, Julia, R, etc.).
Schema validation tools in major languages to ensure correct encoding and robust interoperability (Coll et al., 15 Jul 2025).

5. Applications and Impact

HIF has been demonstrated through case studies where publication-based hypergraph datasets (e.g., linking papers, authors, institutions, funding information) are encoded and analyzed using different platforms. Tasks such as community detection, motif enumeration, and centrality computation become accessible across analytical libraries without ad hoc data conversion (Coll et al., 15 Jul 2025).

A typical workflow:

Encode complex interactions (e.g., publication coauthorship, with metadata annotations) as HIF.
Analysis in one tool (e.g., motif analysis in XGI), further exploration in another (e.g., visualization in HyperNetX).
Seamless exchange enables joint analysis pipelines across otherwise isolated software ecosystems, facilitating reproducibility and reducing duplicated engineering work.

The provision for rich annotation and complexity directly benefits studies in bibliometrics, molecular reaction modeling, social group analysis, biological interaction networks, and other domains where higher-order relations are central.

HIF is positioned analogously to GraphML (for graphs) and ONNX (for neural network models), providing not only a structural interchange standard but also a vehicle for reproducible computational science (Coll et al., 15 Jul 2025). Its focus on explicit higher-order relationships allows migration beyond forced reduction to pairwise formats, preserving the true topology of multidimensional phenomena.

Ongoing and future developments include:

Support for efficient serialized formats (e.g., JSON Lines for streaming), and database-oriented access (prospective GraphQL integration).
Full coverage of emerging network types (ordered, partially ordered, temporal, multiplex).
Community-driven schema evolution with consistent backward compatibility.

A plausible implication is the consolidation of research infrastructure for higher-order modeling, both improving reproducibility and broadening the accessibility of advanced network methods.

While HIF provides a practical interoperability layer, its mathematical foundation is consistent with established hypergraph theory, including undirected, directed, k-uniform, and simplicial complex structures. By enabling standardized data exchange, HIF also directly supports advances in areas such as:

Mapping of relational and semantic models onto hypergraph structures (1105.6118, Munshi et al., 2013).
Direct representation of multi-adic relationships crucial for complex co-occurrence networks and knowledge discovery workflows (Ouvrard et al., 2018).
Annotation and joint analysis of semantic and temporal dynamics, facilitating advanced tasks in natural language generation, action recognition, and beyond (Wang et al., 2023, Raman et al., 2023).

HIF thus operates at the intersection of network science, data modeling, and scientific computing, serving as both a technical standard and an enabler of methodological advances across disciplines.