Targeted Disruption of Hypernetworks via Spectral Partitioning

TL;DR

This paper investigates hyperedge removal strategies in hypergraphs to suppress contagion, revealing that spectral clustering-based targeting is effective in some topologies but not universally.

Contribution

It introduces a spectral overlap-based hyperedge ranking method and compares its effectiveness to random removal across different hypergraph models.

Findings

Spectral clustering-based hyperedge removal reduces contagion in Erd ext{"o}s--Rényi hypergraphs.

In Watts--Strogatz and Barabási--Albert hypergraphs, random removal performs as well or better.

Structural hyperedge importance does not always correlate with optimal contagion suppression.

Abstract

We study hyperedge-removal strategies for suppressing contagion on synthetic hypergraphs. Hypergraphs are generated from Erd\H{o}s--R\'enyi, Barab\'asi--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 Erd\H{o}s--R\'enyi case, cut-persistence targeting reduces final infection size more than random hyperedge removal. In the Watts--Strogatz and Barab\'asi--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.