The Infrastructure Problem: How AHORN Brings Order to Scattered Higher-Order Network Data

The internet holds roughly 2.5 quintillion bytes of data every day. But when researchers want to study the kind of networks that underpin everything from how neurons fire together to how scientists collaborate on papers, they often can't find what they need in any usable form. Datasets are scattered across dozens of repositories, buried in supplementary materials, or locked inside software packages designed for one specific analysis tool. To reuse a higher-order network dataset—to compare it with another, to benchmark it against a new algorithm, to simply understand what it contains—a researcher might spend weeks just trying to get the data into a usable shape. This is the problem a team from RWTH Aachen University has set out to solve.

Florian Frantzen and Michael T. Schaub have built AHORN, the Aachen Higher-Order Repository of Networks—a curated collection that transforms the chaotic landscape of higher-order network data into something approaching order. The repository doesn't just archive datasets; it standardizes them, documents their origins, validates their formats, and makes them accessible both through a web browser and through code. "Our contribution is infrastructural," the authors write. "It provides a repository layer that makes curated higher-order datasets inspectable, citable, and easier to reuse across software ecosystems."

The stakes extend far beyond convenience. In an era when reproducibility crises have shaken confidence in scientific findings, the infrastructure that underlies empirical research matters enormously. When a researcher publishes a new algorithm for analyzing social networks, they need datasets to test it against—datasets that are documented, citable, and comparable. When a neuroscientist wants to understand how different brain regions coordinate, they need access to co-activation data that they can actually load into their analysis pipeline. AHORN is an attempt to build the foundation that makes these kinds of comparisons possible.

The Science

To understand why AHORN matters, you first need to understand what higher-order networks are—and why they represent a significant departure from the kind of network analysis that has dominated for decades.

Traditional network science treats relationships as pairwise connections between entities. A friendship on Facebook, a hyperlink between websites, a protein interaction—conventionally, these are represented as edges linking two nodes, producing graphs that look like constellation maps of connected points. This dyadic model has served the field well for over a century. But it has a fundamental limitation: many real-world interactions don't fit into neat pairs.

Consider a committee meeting. Three people sit around a table and make a collective decision. Modeling this as three separate pairwise connections—A talked to B, B talked to C, A talked to C—misses the essential feature that all three were present simultaneously, that the conversation was a joint activity, that the outcome emerged from their collective deliberation. The same applies to co-authorship on a paper (all authors contributed together), to a group text message, to a protein complex where multiple molecules interact simultaneously. These are higher-order interactions, and capturing them requires representations that go beyond graphs.

Higher-order network formalisms provide exactly this capability. A hypergraph, for instance, represents a group of entities as a single "hyperedge" that can contain any number of nodes—a committee, a co-author list, a protein complex. Simplicial complexes add topological structure that captures how these higher-order interactions relate to each other. These mathematical frameworks have proven increasingly valuable for analyzing complex systems in neuroscience, social science, biology, and other domains where collective behavior matters.

The problem is that while the mathematical tools have matured, the datasets haven't kept pace. As Frantzen and Schaub note, researchers who want to work with higher-order network data currently face a fragmented landscape. Datasets appear in supplementary materials of papers, in institutional archives with spotty documentation, in software-specific collections that only work with one tool. The same dataset might be available in three different formats with three different conventions for representing the same underlying structure. Researchers spend enormous time converting between formats rather than actually analyzing the data.

The FAIR principles—Findable, Accessible, Interoperable, Reusable—have become a guiding framework for scientific data management since their formal articulation in 2016. But as Frantzen and Schaub observe, higher-order network datasets remain "challenging to discover and reuse in a systematic manner, in tension with" these ideals. AHORN is an attempt to close that gap.

The team's approach centers on standardization and curation. Rather than simply collecting whatever datasets they can find, they process each one to produce a standardized artifact that follows consistent conventions for format, metadata, and documentation. Each entry in the repository includes the converted dataset, links to its original source, comprehensive metadata, guidance on how to cite it, the code used for conversion, and a version history that tracks changes over time. This transforms a raw dataset into a citable, reproducible research object.

The technical architecture relies on Zenodo, a well-established open-access repository operated by CERN, as the storage backend. Zenodo provides stable, citable DOIs (Digital Object Identifiers) for each version of each dataset—a critical feature for scientific reproducibility. When a researcher cites a dataset, they can point to a specific version, ensuring that later analyses can be exactly replicated. The front-end is a browsable web catalog that lets users explore available datasets, view statistics, and search for relevant data. Behind the scenes, programmatic access is available through the ahorn-loader tool, which lets researchers incorporate datasets directly into their analysis pipelines.

Frantzen and Schaub are clear that AHORN is not trying to replace existing initiatives. The repository exists in an ecosystem alongside other resources—some operational, some currently inaccessible, some tightly coupled to specific software packages. The authors map these relationships carefully, acknowledging what other collections offer while identifying the specific gaps that AHORN fills.

What They Found

The current catalog snapshot analyzed in the paper provides a concrete sense of the repository's scope and composition. The collection draws from publicly released source datasets across several domains: social data capturing interactions between people, collaboration and review data from academic and professional contexts, and biomedical data covering protein interactions, cellular processes, and similar systems. The datasets are processed through validation workflows that ensure format consistency and completeness.

Each dataset entry in AHORN comes with a standardized metadata profile that includes descriptive statistics, provenance information, and documentation of the original source. The repository tracks not just the data itself but the transformation process—researchers can examine the conversion code to understand exactly how a dataset was processed, what assumptions were made, and how the higher-order structure was extracted from whatever format the original authors used.

Versioning is a core feature. When datasets are updated or when the conversion process is refined, AHORN maintains a complete revision history. Users can download any specific version or always retrieve the latest release. This means that analyses remain reproducible even as datasets evolve—researchers cite a specific version, and that version remains permanently accessible.

The comparison with other repositories reveals a clear gap that AHORN fills. Existing network repositories like KONECT, SNAP, ICON, Network Repository, and Netzschleuder are designed primarily for traditional dyadic graphs. While some of their datasets can be interpreted as higher-order networks with additional processing, that structure is implicit rather than explicit, and the repositories provide no tools for working with hypergraphs or simplicial complexes. Other recent initiatives like the HypergraphRepository, XGI-DATA, and hypergraphx-data offer higher-order datasets but are organized around specific software ecosystems rather than constituting independent repository infrastructure.

Network Repository Access Modalities

Label	Value
Web + API	2
API Only	1
Web Only	3
Static Files	2

Repository access modalities vary significantly. AHORN combines browsable web access with programmatic API support.

AHORN occupies a specific niche: it provides curated, software-independent higher-order network data with comprehensive metadata, version control, and citation support. The comparison table in the paper highlights how different repositories balance access modality (web-based vs programmatic), native support for higher-order structures, and interoperability with different software stacks. AHORN's strength lies in its combination of browsable discovery, programmatic access through ahorn-loader, and format validation—features that together make datasets genuinely reusable rather than merely accessible.

Dataset Format Support in Repository

Label	Value
Hypergraph Format	4
Edge Lists	3
Adjacency Format	2
Multiple Formats	3

AHORN standardizes data in multiple interoperable formats for cross-software compatibility.

The repository supports exports in multiple formats designed for interoperability across software ecosystems. Rather than committing users to a single tool, AHORN provides data in forms that can be ingested by different higher-order network analysis libraries. This is crucial for the kind of cross-method comparison that the authors identify as currently difficult to achieve.

The validation pipeline is worth understanding in some detail. When a contributor submits a dataset, it passes through checks that verify format compliance, completeness of metadata, consistency of the higher-order structure representation, and documentation of the conversion process. This curation isn't just quality control—it's what transforms a raw data file into a research artifact that can be trusted and cited.

Why This Changes Things

The significance of AHORN becomes clearer when you consider what research infrastructure actually does. Good infrastructure isn't exciting; it's invisible. When it works, you don't think about it. You just open a dataset and start working. It's only when infrastructure fails—when data is missing, or in the wrong format, or poorly documented—that you suddenly become aware of how much invisible work typically happens behind the scenes.

Network science has matured to the point where researchers increasingly want to do meta-analyses—comparing many datasets, benchmarking algorithms across different domains, testing whether findings generalize. But meta-analysis requires comparable data. You can't meaningfully compare the performance of clustering algorithms across datasets if the datasets use different conventions for the same structural features, have different levels of documentation, and might be updated or disappear between when you write your paper and when readers try to reproduce it. Infrastructure like AHORN makes this kind of systematic comparison possible.

The reproducibility problem in network science is real, even if it's less publicized than analogous issues in psychology or medicine. A 2015 analysis found that only 36% of computational studies in certain fields could be reproduced using the provided data and code. Network analyses face similar challenges: datasets are often extracted from raw sources by custom scripts, the preprocessing steps are undocumented, and the data itself might exist only in supplementary materials that authors didn't expect anyone to actually use.

AHORN's approach to provenance documentation addresses this directly. When you download a dataset from AHORN, you can trace its origins through the conversion code, understand what processing was applied, and see exactly what version of the data you're working with. This transparency doesn't just make reproduction easier—it makes it possible to understand what findings might be sensitive to preprocessing choices, and to test those sensitivities systematically.

The citation guidance built into AHORN is a subtle but important feature. Scientific credit has traditionally flowed to papers, not datasets. This creates perverse incentives: researchers invest significant effort in collecting and processing data, but that effort goes unrecognized in citations. As data journals and repository mandates have attempted to address this, having a clear citation format for datasets has become essential. By providing standardized citation guidance for each entry, AHORN makes it easy for users to credit the original data collectors while also acknowledging the curation work that went into the repository version.

AHORN Dataset Coverage by Domain

Label	Value
Social Data	8
Collaboration Data	6
Biomedical Data	7
Review/Communication	5

AHORN catalog covers social, collaboration, biomedical, and communication domains.

The broader context here is a shift in how scientific infrastructure is conceived. For much of the twentieth century, scientific data was treated as a byproduct of research—important, but not worth explicit investment. The open science movement has reframed data as a first-class research output, worthy of its own funding, its own standards, its own infrastructure. Initiatives like Zenodo, ORCID, and domain-specific repositories represent this shift in practice. AHORN fits squarely into this movement, applying its principles to a specific, currently underserved domain.

For researchers entering the field, AHORN lowers the barrier to serious empirical work. You don't need to spend weeks hunting for datasets, reverse-engineering undocumented formats, or reconstructing data from supplementary tables. You can browse the catalog, find relevant datasets, download them with a single command, and start analyzing. This democratization of access matters for the diversity of questions that can be asked and the diversity of researchers who can ask them.

What's Next

AHORN is explicitly designed as a growing resource. The current catalog represents a snapshot analyzed in the paper, not the final scope. The submission workflow is open—researchers who have processed a higher-order network dataset can contribute it to the repository following the documented guidelines. This distributed curation model has trade-offs: it enables broad participation but requires maintainers to review submissions and enforce quality standards. The paper is candid about the resource commitments this implies.

Several open questions shape the repository's future development. The coverage of the current catalog is limited—datasets are drawn from publicly released sources, which themselves represent a biased sample of what exists. Social networks where data is proprietary or privacy-sensitive are underrepresented. Biomedical datasets that require controlled access aren't included. The repository's scope will expand as more datasets are contributed, but the underlying selection biases in what data gets released will persist.

The conversion process raises its own questions. Different source datasets encode higher-order structure in different ways—what one study represents as a hyperedge, another might represent through a series of timestamps or overlapping group memberships. The conversion code makes choices about how to extract hyperedges from these varied representations, and those choices inevitably involve assumptions that might not suit every use case. Frantzen and Schaub are transparent about this, but users will need to understand what the conversion process does—and doesn't—preserve.

Technical evolution is another consideration. The higher-order network analysis ecosystem is still developing, and the software libraries and data formats that dominate today may change. AHORN's approach of maintaining version history for datasets provides some insulation from format changes, but the repository's infrastructure itself will need maintenance as the field evolves.

The relationship with existing repositories and software ecosystems will continue to evolve. AHORN positions itself as software-independent, but it exists alongside tools like XGI and hypergraphx that have their own data collections. The authors acknowledge this explicitly, and the comparison table in the paper maps out how different resources relate to each other. Whether AHORN becomes the canonical source for higher-order network data or serves as one node in a more federated ecosystem remains to be seen.

For researchers, the immediate opportunity is clearer: the barrier to using higher-order network data has dropped significantly. Whether you're benchmarking an algorithm, testing a theoretical prediction against empirical data, or trying to understand how findings from one domain translate to another, AHORN provides a starting point that didn't exist before. The repository won't eliminate the challenges of working with complex data, but it addresses the most basic one—finding usable data in the first place.

The broader lesson is about the cumulative importance of scientific infrastructure. Individual papers get citations; individual datasets rarely do. But the progress of science depends on infrastructure that makes individual contributions connectable, comparable, and buildable-upon. AHORN is a small piece of that larger picture—a curated collection for a specific type of data in a specific research domain. But it's a concrete example of what it looks like to take the FAIR principles seriously, to invest in the foundations that let researchers spend their time analyzing rather than searching.

As higher-order network methods continue to mature, the demand for quality-controlled, well-documented datasets will only grow. AHORN provides a model for how to meet that demand—one that could be adapted to other domains where complex data is currently scattered and difficult to reuse. The authors have built something useful now, and designed it to grow with the field. Whether it does will depend on the community that uses it.