Directionality and node heterogeneity reshape criticality in hypergraph percolation

TL;DR

This paper develops a message-passing framework for percolation in directed, heterogeneous hypergraphs, revealing how their features fundamentally alter critical behavior and robustness in complex networks.

Contribution

It introduces a novel theoretical approach that explicitly incorporates directionality and heterogeneity, demonstrating their impact on hypergraph percolation criticality.

Findings

Hypergraph features reshape critical exponents in percolation.

Theoretical predictions validated on synthetic and real metabolic networks.

Directionality and heterogeneity influence network robustness.

Abstract

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.