Directionality and node heterogeneity reshape criticality in hypergraph percolation
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| Format: | Preprint |
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2026
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| _version_ | 1866908794132365312 |
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| author | Sun, Yunxue Liu, Xueming Bianconi, Ginestra |
| author_facet | Sun, Yunxue Liu, Xueming Bianconi, Ginestra |
| contents | Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of others only weakens interactions. Metabolic reaction networks offer an intuitive example of such asymmetric dependencies. Here we develop a message-passing and statistical mechanics framework for percolation in directed hypergraphs that explicitly incorporates directionality and node heterogeneity. Remarkably, we show that these hypergraph features have a fundamental effect on the critical properties of hypergraph percolation, reshaping criticality in a way that depends on network structure. Specifically, we derive anomalous critical exponents that depend on whether node or hyperedge percolation is considered in maximally correlated, heavy-tailed regimes. These theoretical predictions are validated on synthetic hypergraph models and on a real directed metabolic network, opening new perspectives for the characterization of the robustness and resilience of real-world directed, heterogeneous higher-order networks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_20726 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Directionality and node heterogeneity reshape criticality in hypergraph percolation Sun, Yunxue Liu, Xueming Bianconi, Ginestra Disordered Systems and Neural Networks Statistical Mechanics Physics and Society Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of others only weakens interactions. Metabolic reaction networks offer an intuitive example of such asymmetric dependencies. Here we develop a message-passing and statistical mechanics framework for percolation in directed hypergraphs that explicitly incorporates directionality and node heterogeneity. Remarkably, we show that these hypergraph features have a fundamental effect on the critical properties of hypergraph percolation, reshaping criticality in a way that depends on network structure. Specifically, we derive anomalous critical exponents that depend on whether node or hyperedge percolation is considered in maximally correlated, heavy-tailed regimes. These theoretical predictions are validated on synthetic hypergraph models and on a real directed metabolic network, opening new perspectives for the characterization of the robustness and resilience of real-world directed, heterogeneous higher-order networks. |
| title | Directionality and node heterogeneity reshape criticality in hypergraph percolation |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Physics and Society |
| url | https://arxiv.org/abs/2601.20726 |