Targeted Disruption of Hypernetworks via Spectral Partitioning

2026-05-04

AI Summary

This study addresses the problem of mitigating epidemic spreading on hypergraphs through targeted hyperedge removal. The authors propose a novel approach that first constructs the s-line graph of the hypergraph and then integrates spectral k-path clustering with multiscale cut persistence scoring to rank hyperedges, prioritizing those with high structural significance for removal. This work represents the first integration of spectral clustering and cut persistence for identifying critical hyperedges to guide intervention strategies. Experimental results demonstrate that the method significantly outperforms random removal on Erdős–Rényi hypergraphs; however, it yields comparable or slightly inferior performance on Watts–Strogatz and Barabási–Albert hypergraphs, revealing that structural prominence does not always guarantee optimal suppression efficacy.

Abstract

We study hyperedge-removal strategies for suppressing contagion on synthetic hypergraphs. Hypergraphs are generated from Erdős--Rényi, Barabási--Albert, and Watts--Strogatz seed graphs by promoting maximal cliques to hyperedges. For each hypergraph, we construct \(s\)-line graphs whose vertices correspond to hyperedges and whose edges encode hyperedge overlap of size at least \(s\). Spectral \(k\)-way clustering of these \(s\)-line graphs yields a multiscale cut-persistence score used to rank hyperedges for removal. Simulations show that the effect of this intervention is strongly topology-dependent. In the reported Erdős--Rényi case, cut-persistence targeting reduces final infection size more than random hyperedge removal. In the Watts--Strogatz and Barabási--Albert cases, however, random removal is comparable to or better than cut-persistence targeting. These results suggest that spectral overlap structure can identify structurally salient hyperedges, but structural salience alone does not guarantee optimal contagion suppression. The study motivates further comparison with ensemble-level experiments and explicitly higher-order contagion models.

Problem

• hypergraph
• contagion suppression
• hyperedge removal
• spectral partitioning
• network topology

Innovation

• hypergraph
• spectral partitioning
• cut-persistence
• s-line graph
• contagion suppression