Beyond trivial edges: A fractional approach to cohesive subgraph detection in hypergraphs

Abstract

Hypergraphs can capture high-order relationships in complex systems, yet large hyperedges often dilute cohesive structures by incorporating loosely related nodes. To address this, we propose a fraction-based cohesive subgraph model, called the (k,g,p)-core, which extends existing support-based frameworks by introducing a user-defined fraction threshold. This threshold effectively filters out hyperedges deemed too large to convey meaningful connections, thereby emphasising high-quality, context-specific relationships. We devise two algorithms – Naïve and Advanced – to efficiently compute the (k,g,p)-core. The Advanced algorithm leverages lazy update strategies to avoid repeated neighbour recalculations, reducing computational overhead. Experimental evaluations on real-world datasets show that our method not only preserves the accuracy of cohesive subhypergraph discovery but also improves computational efficiency by over 50% compared to baseline approaches. Our findings demonstrate the importance of fraction-based constraints in refining subhypergraph discovery, opening avenues for more robust hypergraph analysis in domains such as recommendation systems, anomaly detection, and community detection