# Community and hyperedge inference in multiple hypergraphs

arXiv: https://arxiv.org/abs/2505.04967 · HTML: https://mlsanity.com/paper/2505.04967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 19 of 19)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys](https://mlsanity.com/paper/1506.03645/) (2015)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration](https://mlsanity.com/paper/1909.06503/) (2019)
- [Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers](https://mlsanity.com/paper/1409.7017/) (2014)
- [Spectral Detection on Sparse Hypergraphs](https://mlsanity.com/paper/1507.04113/) (2015)
- [Recovering communities in the general stochastic block model without knowing the parameters](https://mlsanity.com/paper/1506.03729/) (2015)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Three hypergraph eigenvector centralities](https://mlsanity.com/paper/1807.09644/) (2018)
- [Node and Edge Nonlinear Eigenvector Centrality for Hypergraphs](https://mlsanity.com/paper/2101.06215/) (2021)
- [Social Hash Partitioner: A Scalable Distributed Hypergraph Partitioner](https://mlsanity.com/paper/1707.06665/) (2017)
- [Random walks and community detection in hypergraphs](https://mlsanity.com/paper/2010.14355/) (2020)
- [Structure and inference in hypergraphs with node attributes](https://mlsanity.com/paper/2311.03857/) (2023)
- [Multilayer Networks in a Nutshell](https://mlsanity.com/paper/1804.03488/) (2018)
- [A framework to generate hypergraphs with community structure](https://mlsanity.com/paper/2212.08593/) (2022)
- [Community Detection in Large Hypergraphs](https://mlsanity.com/paper/2301.11226/) (2023)
- [Modelling Non-Linear Consensus Dynamics on Hypergraphs](https://mlsanity.com/paper/2007.09391/) (2020)
- [Hypergraph Partitioning for Sparse Matrix-Matrix Multiplication](https://mlsanity.com/paper/1603.05627/) (2016)

## Abstract (arXiv)

Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding relationship between genes and their protein products, drive the establishment of interconnections between multiple hypergraphs. Here, we demonstrate how to utilize those interconnections between multiple hypergraphs to synthesize integrated information from multiple higher-order systems, thereby enhancing understanding of underlying structures. We propose a model based on the stochastic block model, which integrates information from multiple hypergraphs to reveal latent high-order structures. Real-world hyperedges exhibit preferential attachment, where certain nodes dominate hyperedge formation. To characterize this phenomenon, our model introduces hyperedge internal degree to quantify nodes' contributions to hyperedge formation. This model is capable of mining communities, predicting missing hyperedges of arbitrary sizes within hypergraphs, and inferring inter-hypergraph edges between hypergraphs. We apply our model to high-order datasets to evaluate its performance. Experimental results demonstrate strong performance of our model in community detection, hyperedge prediction, and inter-hypergraph edge prediction tasks. Moreover, we show that our model enables analysis of multiple hypergraphs of different types and supports the analysis of a single hypergraph in the absence of inter-hypergraph edges. Our work provides a practical and flexible tool for analyzing multiple hypergraphs, greatly advancing the understanding of the organization in real-world high-order systems.