Hypergraphx-data: Higher-Order Networks
- Hypergraphx-data is a curated repository of real-world higher-order network datasets that preserve group interactions across various domains.
- It standardizes data with multi-level metadata, provenance tracking, version control, and interoperability with the Hypergraphx software suite.
- The repository enables reproducible empirical research by addressing the limitations of dyadic graph representations in complex systems.
Hypergraphx-data is a curated repository of real-world higher-order network datasets designed for systems in which interactions are not merely pairwise but can involve arbitrary groups of entities. It was introduced to fill a gap left by widely used repositories centered on dyadic graphs, and it combines dataset collection, standardization, preservation, provenance tracking, versioning, integrity verification, and software interoperability for empirical hypergraph research. At publication time, the repository contains 103 datasets spanning 10 domains, is available at https://hgx-team.github.io/hypergraphx-data, and is positioned as a companion to the Hypergraphx (HGX) software library for higher-order network analysis (Lotito et al., 18 May 2026).
1. Rationale and scientific role
Hypergraphx-data was created in response to a structural limitation in the data ecosystem of network science. Repositories such as SNAP, Netzschleuder, KONECT, and the Network Repository have made graph datasets broadly accessible, but they are built primarily around traditional dyadic graphs, where each edge connects exactly two nodes. That orientation is poorly suited to empirical systems whose native relational primitive is many-body interaction rather than pairwise linkage. The repository therefore addresses data types such as coauthorship teams, group meetings, metabolic reactions, multi-recipient emails, and multi-party financial transactions in a form that preserves their polyadic structure (Lotito et al., 18 May 2026).
The paper frames this intervention as solving two related problems. The first is a data-model problem: conventional graph repositories do not provide a standardized home for non-dyadic relational data. The second is a scientific workflow problem: real-world hypergraph datasets are fragmented across domain repositories, supplementary materials, and code archives attached to individual studies, and are often distributed only as bipartite data, event logs, or dyadic projections that discard crucial higher-order structure. Hypergraphx-data centralizes such datasets, reconstructs or preserves higher-order interactions where possible, standardizes formats, maintains versions, and adds metadata and provenance information. This suggests a repository intended not simply as storage, but as infrastructure for reproducible empirical comparison of higher-order methods (Lotito et al., 18 May 2026).
2. Coverage, domains, and supported higher-order structures
At publication time, Hypergraphx-data contains 103 datasets spanning 10 domains. The covered application areas include social systems, technological systems, ecology, biology, and finance, and the repository is intended to include both natural and artificial systems wherever higher-order interactions matter. The cited examples include face-to-face interaction data from schools, hospitals, offices, and conferences; coauthorship networks in which a paper induces a hyperedge joining all its authors; Q&A forum data; voting or collective decision datasets; email data with multiple recipients; Bitcoin transaction datasets involving multiple senders and receivers; animal proximity or group interaction data; gene–disease associations; drug association datasets; metabolic reaction systems; hypergraphs built from IMDB, where movies define hyperedges over actors; and hypergraphs built from ArXiv, where each paper defines a hyperedge over coauthors (Lotito et al., 18 May 2026).
The repository supports several hypergraph configurations beyond the simplest undirected set-based case:
| Configuration | Repository support |
|---|---|
| Undirected hypergraphs | Hyperedge as a set of nodes |
| Directed hypergraphs | Source and target node sets |
| Weighted hypergraphs | Numerical hyperedge weights |
| Temporal hypergraphs | Timestamps on hyperedges |
| Multiplex hypergraphs | Layered relations on the same node set |
The paper is explicit that these structures are presented conceptually rather than through a full formal mathematical section. It does not provide explicit LaTeX definitions such as , nor formal symbolic definitions for temporal or multiplex indexing. The main formal notation supplied concerns counts and operational conventions: the repository contains $103$ datasets across $10$ domains, dataset versions follow major.minor.patch, and integrity verification uses SHA-256 (Lotito et al., 18 May 2026).
3. Data model, metadata, and distribution formats
Each dataset includes both relational structure and metadata, with metadata organized at three levels. At the system level, examples include dataset name, domain, version, source, and global summary statistics such as average hyperedge size and maximum hyperedge size. At the node level, metadata may encode attributes such as age, sex, molecular type, and names or identifiers. At the interaction level, hyperedge metadata may include weight, timestamp, and categorical or domain-specific labels, such as the field of a paper or the genre of a movie. This multi-level metadata design supports not only structural analysis but also contextual interpretation and attribute-aware methods (Lotito et al., 18 May 2026).
Hypergraphx-data distributes datasets in two formats. The first is an open JSON format, intended to be human-readable and interoperable. In this representation, datasets contain global metadata, a collection of nodes represented as distinct objects with attributes, and a collection of hyperedges represented as distinct objects listing member nodes plus associated attributes. For directed hypergraphs, the paper implies that source and target node roles are represented in the hyperedge description, and temporal or multiplex information appears as hyperedge attributes such as timestamps or layer labels. The paper notes that a JSON schema exists, but it does not print a literal field-by-field schema or a complete field dictionary (Lotito et al., 18 May 2026).
The second format is a binary format optimized for Hypergraphx, storing hypergraph data as serialized Python arrays and dictionaries. Its purpose is performance. The paper reports that JSON is on average 1.5 larger and about 5 slower to load. The benchmark conditions are specified in detail: Ubuntu 24.04.3 LTS, x86_64, 8 CPU cores, approximately 94 GiB RAM, Python 3.10, single-threaded runs, testing the full dataset catalog, averaging loading times over ten runs, and measuring storage sizes on uncompressed files. In practical terms, the repository therefore distinguishes between a self-descriptive exchange format and a high-performance local-analysis format (Lotito et al., 18 May 2026).
4. Dataset construction, provenance, and reproducibility controls
The repository uses three main dataset-construction pipelines. First, some datasets are built from raw public sources; the paper gives IMDB and ArXiv as examples. Second, many datasets are collected from prior methodological literature and then standardized. Third, some are converted from non-hypergraph source formats when higher-order structure is natural, including bipartite incidence data. The paper also highlights a more delicate case: some datasets, such as SocioPatterns face-to-face contact records, are distributed as dyadic temporal contacts, and their original polyadic group structure can be partially reconstructed using fine-grained timing and clique-based heuristics over co-occurring dyadic ties. The paper explicitly describes this as a heuristic inference of group structure, which is an important qualification on the status of some higher-order datasets (Lotito et al., 18 May 2026).
A major feature of Hypergraphx-data is its emphasis on provenance, attribution, and reproducibility. Each dataset includes credits to the original work, citation guidance, easy access to BibTeX, licensing information, redistribution rights, links to the exact raw data source, and the scripts used to construct the distributed hypergraph objects. The last element is especially consequential, because the repository does not only provide processed outputs; it also provides the transformation path from raw source data to hypergraph representation when the repository authors derived the dataset themselves (Lotito et al., 18 May 2026).
Versioning and integrity verification are handled with unusually explicit technical conventions. Hypergraphx-data uses semantic versioning with identifiers of the form major.minor.patch. Major changes alter structural properties of the networked system, such as adding or removing nodes or links; minor changes add non-structural enhancements such as metadata; patch changes correct small errors such as attribute mistakes. Older versions remain available and identifiable, and each dataset has a detailed changelog documenting additions, updates, and deprecations. Each dataset version is also associated with a SHA-256 cryptographic hash, stored in immutable release records together with metadata and changelogs. A local file can therefore be checked against a repository reference hash both for integrity checking and version disambiguation (Lotito et al., 18 May 2026).
5. Access, software workflow, and interoperability
Hypergraphx-data is designed to be usable both from the website and from code. The homepage introduces the scope of the repository and highlights updates such as recently added datasets or version changes. The dataset browser supports search and filtering, including filters by domain, number of nodes, number of hyperedges, the presence of temporal annotations, and whether hyperedges are weighted. Each dataset has a dedicated detail page exposing metadata and characteristics, structural summary statistics, available formats, current and older versions, source references in BibTeX, and basic visualizations such as hyperedge size distributions and hyperdegree distributions. The paper does not specify the frontend or backend stack, and it does not define the plotting algorithms used for these visualizations (Lotito et al., 18 May 2026).
The core workflow described in the paper is repository-centric. A typical sequence is: browse or filter datasets on the website; inspect metadata, statistics, and references on the detail page; download the data in JSON or binary form; load local files with load_hypergraph() or fetch them directly with load_hypergraph_from_server(); and, if needed, export or bridge them through to_hif() to another higher-order library. This places Hypergraphx-data within a software stack rather than treating it as a static archive (Lotito et al., 18 May 2026).
Interoperability is a central design goal. Hypergraphx supports conversion through the Hypergraph Interchange Format (HIF) using to_hif(), enabling sharing with other HIF-compatible tools, including XGI, HyperNetX, and SimpleHypergraphs, without custom schema readers (Lotito et al., 18 May 2026). This is consistent with the broader HIF effort described for HyperNetX, where a JSON-based interchange format is intended to preserve metadata on nodes, hyperedges, and incidences across libraries (Praggastis et al., 2023). Hypergraphx-data is also part of the larger Hypergraphx ecosystem, which had already been presented as a higher-order analysis library accompanied by an extended data repository and support for weighted, directed, signed, temporal, and multiplex group interactions (Lotito et al., 2023).
6. Position in the higher-order ecosystem and future directions
The repository’s distinguishing feature is not merely that it offers more datasets, but that it is organized around a different relational primitive. Traditional graph repositories remain highly useful when the data can be represented faithfully as edge lists or ordinary graphs. Hypergraphx-data is built around the claim that many empirical systems are fundamentally composed of group interactions, and that forcing them into pairwise projections can erase structure, distort dynamics, and produce unfair benchmarks for algorithms designed for hypergraphs. Its standardized higher-order formats, preserved provenance, metadata richness, version control, and integrity checks are intended to make it possible to compare methods on common data without repeatedly rebuilding import pipelines or reconstructing polyadic interactions from scratch (Lotito et al., 18 May 2026).
The paper explicitly situates Hypergraphx-data as complementary to Hypergraphx, XGI-data, HypergraphRepository, the Cornell hypergraph data page, and HIF-compatible libraries such as XGI, HyperNetX, and SimpleHypergraphs (Lotito et al., 18 May 2026). A plausible implication is that the repository is meant to function less as a closed platform than as a standardizing node within an emerging interoperable higher-order data ecosystem.
The authors also state several limitations and future directions. Planned developments include continued addition of datasets, more interactive hypergraph visualization tools, richer computed statistics tailored to temporal, directed, and multiplex hypergraphs, a more robust binary format with safer loading and faster I/O, and stronger compatibility with the Hypergraph Interchange Format, including support for more hypergraph types. They also identify the need for common benchmarks for tasks such as motif mining, community detection, dimensionality reduction and filtering, influence maximization, and shortest-path computation, in a role analogous to what the Open Graph Benchmark has played for graph machine learning (Lotito et al., 18 May 2026). In that sense, Hypergraphx-data defines not only a repository, but also an agenda for how empirical higher-order network research may become more standardized, comparable, and reproducible.