# Inference of hyperedges and overlapping communities in hypergraphs arXiv: https://arxiv.org/abs/2204.05646 ยท HTML: https://mlsanity.com/paper/2204.05646/ ## Key facts - Cited by 13 papers in the map (data through 14 Oct 2026). - Builds on 36 of its 77 references that are in the map. - First posted on arXiv 12 Apr 2022. ## Builds on (most cited first, 30 of 36) - [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020) - [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016) - [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016) - [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018) - [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018) - [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021) - [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) - [The ground truth about metadata and community detection in networks](https://mlsanity.com/paper/1608.05878/) (2016) - [Clustering in graphs and hypergraphs with categorical edge labels](https://mlsanity.com/paper/1910.09943/) (2019) - [Structure and inference in annotated networks](https://mlsanity.com/paper/1507.04001/) (2015) - [Evolutionary dynamics of higher-order interactions in social networks](https://mlsanity.com/paper/2001.10313/) (2020) - [The why, how, and when of representations for complex systems](https://mlsanity.com/paper/2006.02870/) (2020) - [Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data](https://mlsanity.com/paper/1601.01704/) (2016) - [Memory in network flows and its effects on spreading dynamics and community detection](https://mlsanity.com/paper/1305.4807/) (2013) - [Hypergraph reconstruction from network data](https://mlsanity.com/paper/2008.04948/) (2020) - [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) - [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017) - [Random walks on hypergraphs](https://mlsanity.com/paper/1911.06523/) (2019) - [Configuration Models of Random Hypergraphs](https://mlsanity.com/paper/1902.09302/) (2019) - [Community detection with node attributes in multilayer networks](https://mlsanity.com/paper/2004.09160/) (2020) - [The importance of the whole: topological data analysis for the network neuroscientist](https://mlsanity.com/paper/1806.05167/) (2018) - [Three hypergraph eigenvector centralities](https://mlsanity.com/paper/1807.09644/) (2018) - [Causality-Driven Slow-Down and Speed-Up of Diffusion in Non-Markovian Temporal Networks](https://mlsanity.com/paper/1307.4030/) (2013) - [Cumulative effects of triadic closure and homophily in social networks](https://mlsanity.com/paper/1809.06057/) (2018) - [Node and Edge Nonlinear Eigenvector Centrality for Hypergraphs](https://mlsanity.com/paper/2101.06215/) (2021) - [Random walks and community detection in hypergraphs](https://mlsanity.com/paper/2010.14355/) (2020) - [Spectral Detection of Simplicial Communities via Hodge Laplacians](https://mlsanity.com/paper/2108.06547/) (2021) - [Higher-order motif analysis in hypergraphs](https://mlsanity.com/paper/2108.03192/) (2021) - [Explosive higher-order Kuramoto dynamics on simplicial complexes](https://mlsanity.com/paper/1912.04405/) (2019) ## Built on by (most cited first, 13 of 13) - [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022) - [Normalized mutual information is a biased measure for classification and community detection](https://mlsanity.com/paper/2307.01282/) (2023) - [Structure and inference in hypergraphs with node attributes](https://mlsanity.com/paper/2311.03857/) (2023) - [Broad Spectrum Structure Discovery in Large-Scale Higher-Order Networks](https://mlsanity.com/paper/2505.21748/) (2025) - [Near-Universal Multiplicative Updates for Nonnegative Einsum Factorization](https://mlsanity.com/paper/2602.02759/) (2026) - [Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models](https://mlsanity.com/paper/2401.00688/) (2024) - [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025) - [The Spectral Barycentre of a Set of Graphs with Community Structure](https://mlsanity.com/paper/2502.00038/) (2025) - [Community and hyperedge inference in multiple hypergraphs](https://mlsanity.com/paper/2505.04967/) (2025) - [On the Identifiability of Tensor Ranks via Prior Predictive Matching](https://mlsanity.com/paper/2510.14523/) (2025) - [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025) - [From Representation to Clusters: A Contrastive Learning Approach for Attributed Hypergraph Clustering](https://mlsanity.com/paper/2603.09370/) (2026) - [Implicit Semantic-Aware Communication Based on Hypergraph Reasoning](https://mlsanity.com/paper/2606.20162/) (2026) ## Abstract (arXiv) Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions. Furthermore, our model has an efficient numerical implementation, and it runs faster than dyadic algorithms on pairwise records projected from higher-order data. We apply our method to a variety of real-world systems, showing strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness against addition of noisy hyperedges. Our approach illustrates the fundamental advantages of a hypergraph probabilistic model when modeling relational systems with higher-order interactions.