Cascading failures with group support in interdependent hypergraphs

TL;DR

This paper introduces a hypergraph-based framework to analyze how group support influences the resilience of interdependent systems against cascading failures, revealing critical thresholds and the impact of network topology on robustness.

Contribution

It develops a novel double-layer interdependent hypergraph model incorporating group support, deriving phase transition thresholds and highlighting the effects of network topology on system resilience.

Findings

Increased dependent nodes shift the system from second- to first-order phase transitions.

Scale-free hyperdegree distributions enhance system robustness.

Critical thresholds for initial node survival are analytically derived.

Abstract

The functionality of an entity frequently necessitates the support of a group situated in another layer of the system. To unravel the profound impact of such group support on a system's resilience against cascading failures, we devise a framework comprising a double-layer interdependent hypergraph system, wherein nodes are capable of receiving support via hyperedges. Our central hypothesis posits that the failure may transcend to another layer when all support groups of each dependent node fail, thereby initiating a potentially iterative cascade across layers. Through rigorous analytical methods, we derive the critical threshold for the initial node survival probability that marks the second-order phase transition point. A salient discovery is that as the prevalence of dependent nodes escalates, the system dynamics shift from a second-order to a first-order phase transition. Notably, irrespective of the collapse pattern, systems characterized by scale-free hyperdegree distributions within both hypergraph layers consistently demonstrate superior robustness compared to those adhering to Poisson hyperdegree distributions. In summary, our research underscores the paramount significance of group support mechanisms and intricate network topologies in determining the resilience of interconnected systems against the propagation of cascading failures. By exploring the interplay between these factors, we have gained insights into how systems can be designed or optimized to mitigate the risk of widespread disruptions, ensuring their continued functionality and stability in the face of adverse events.