README.md

---
language:
- en
tags:
- hypergraph
task_categories:
- graph-ml
---
# email-Eu

[Zenodo](https://zenodo.org/records/10155823) | [Cornell](https://www.cs.cornell.edu/~arb/data/email-Eu/) | [Source Paper](https://arxiv.org/abs/1802.06916)

email-Eu is an undirected hypergraph built from anonymized email communication within a large European research institution, designed for higher-order network / hypergraph machine learning. As in real email traffic, a single message can involve multiple people; this dataset captures that group interaction by modeling each email as a hyperedge containing the sender and all recipients (reconstructed by grouping (sender, recipient, timestamp) tuples that share the same timestamp), while nodes represent institutional email addresses restricted to communication among members of the institution (the “core”), with emails involving more than 25 participants excluded.

## Usage

```python
dataset = load_dataset("daqh/email-Eu", split="full")
hypergraphs = [xgi.from_hif_dict(d, nodetype=int, edgetype=int) for d in dataset]
```

## Statistics

<div align="center">
  <table>
    <tbody>
      <tr>
        <td colspan="2" align="center">
          <figure>
            <img src="assets/hypergraph.png">
          </figure>
        </td>
      </tr>
      <tr>
        <td align="center">
          <figure>
            <img src="assets/node-degree-distribution.png">
          </figure>
        </td>
        <td align="center">
          <figure>
            <img src="assets/hyperedge-size-distribution.png">
          </figure>
        </td>
      </tr>
    </tbody>
  </table>
</div>

## Content

The hypergraph is stored in HIF (Hypergraph Interchange Format) as a JSON object, following the schema used to exchange higher-order network data across tools. Concretely, the dataset provides the canonical HIF fields-network-type, metadata, nodes, edges, and incidences-so you can reconstruct the full incidence structure without additional processing.

In addition to the raw hypergraph topology, vector features are provided for both nodes and hyperedges (in their attribute dictionaries), enabling out-of-the-box experimentation with representation learning and downstream tasks:
- Spectral features: eigenvectors of the (hypergraph) Laplacian (computed via sparse eigensolvers).
- [Node2Vec](https://arxiv.org/abs/1607.00653) embeddings: random-walk–based structural embeddings.
- [VilLain](https://dl.acm.org/doi/10.1145/3589334.3645454) embeddings: self-supervised hypergraph representation learning via virtual label propagation.

Basic statistics (as packaged here): 998 nodes, 25027 hyperedges, 20 connected component, largest connected component ratio 0.9809619238476954.

## Citation

```
@article{Benson-2018-simplicial,
 author = {Benson, Austin R. and Abebe, Rediet and Schaub, Michael T. and Jadbabaie, Ali and Kleinberg, Jon},
 title = {Simplicial closure and higher-order link prediction},
 year = {2018},
 doi = {10.1073/pnas.1800683115},
 publisher = {National Academy of Sciences},
 issn = {0027-8424},
 journal = {Proceedings of the National Academy of Sciences}
}
```