Robustness of hypergraph under attack with limited information based on percolation theory

Abstract

Hypergraphs serve as a representative form to display higher-order interactions that persist in the community structure of ecological and social systems. A significant characteristic of these entities is their critical behaviours and robustness in response to aggressive assaults. However, in reality, the network structure may be partially observable, meaning that it is distinct from the assumption of global accessibility under random and deliberate assaults. In this work, we provide a theoretical framework to analyse the changes in the giant component in a hypergraph when subjected to limited information disintegration. Percolation theory is employed to derive the size of the giant component and the critical point. Specifically, we apply the message-passing method based on factor graphs to establish a framework for percolation analysis under limited information attacks. On this basis, the hypergraph structure is accurately described. The advantages lie in avoiding the redundant demands of multiple repetitive experiments. Our study demonstrates the relationship between the diversity of the attacked network and the critical condition. By conducting numerical simulations and theoretical research, we also conclude that controlling the observed size of the network and moderately increasing the average hyperdegree can enhance the robustness of the hypergraph. These findings further indicate the impact of hypergraph topology on the resilience of systems and provide analytical insights for optimizing systems with cost-effectiveness and robustness.