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  • Open Access

Edge correlations and link prediction in growing hypergraphs

Xie He*

Philip S. Chodrow*,†

Peter J. Mucha

  • Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755, USA Microsoft. One Microsoft Way, Redmond, Washington 98052, USA

  • *These authors contributed equally to this work.
  • †Contact author: pchodrow@middlebury.edu
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Phys. Rev. E 112, 024305 – Published 25 August, 2025

DOI: https://doi.org/10.1103/4lkd-mtzq

Abstract

We propose a generative, mechanistic model of temporally evolving hypergraphs in which hyperedges form via noisy copying of previous hyperedges. Our proposed model reproduces several stylized facts from many empirical hypergraphs, is learnable from data, and defines a likelihood over a complete hypergraph rather than ego-based or other subhypergraphs. Analyzing our model, we derive asymptotic descriptions of the node degree, edge size, and edge intersection size distributions in terms of the model parameters. We also show several features of empirical hypergraphs which are and are not successfully captured by our model. We provide a scalable stochastic expectation maximization algorithm with which we can fit our model to hypergraph data sets with millions of nodes and edges. Finally, we assess our model on a hypergraph link prediction task, finding that an instantiation of our model with just 11 parameters can achieve competitive predictive performance with large neural networks.

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Phys. Rev. E 112, 024305– Published 25 August, 2025
  • Received 1 April 2025
  • Accepted 21 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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