Learning Multi-Order Block Structure in Higher-Order Networks

• URL: http://arxiv.org/abs/2511.21350v1
• Date: Wed, 26 Nov 2025 12:56:37 GMT
• Title: Learning Multi-Order Block Structure in Higher-Order Networks
• Authors: Kazuki Nakajima, Yuya Sasaki, Takeaki Uno, Masaki Aida,
• Abstract summary: Higher-order networks are essential for modeling real-world systems involving interactions among three or more entities.<n>A recent simplification, a single-order model, mitigates this complexity by assuming a single affinity pattern governs interactions of all orders.<n>Here, we propose a framework that relaxes this assumption by introducing a multi-order block structure.
• Score: 4.867153093815104
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale organization, yet their extension to hypergraphs involves a trade-off between expressive power and computational complexity. A recent simplification, a single-order model, mitigates this complexity by assuming a single affinity pattern governs interactions of all orders. This universal assumption, however, may overlook order-dependent structural details. Here, we propose a framework that relaxes this assumption by introducing a multi-order block structure, in which different affinity patterns govern distinct subsets of interaction orders. Our framework is based on a multi-order stochastic block model and searches for the optimal partition of the set of interaction orders that maximizes out-of-sample hyperlink prediction performance. Analyzing a diverse range of real-world networks, we find that multi-order block structures are prevalent. Accounting for them not only yields better predictive performance over the single-order model but also uncovers sharper, more interpretable mesoscale organization. Our findings reveal that order-dependent mechanisms are a key feature of the mesoscale organization of real-world higher-order networks.

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