Targeted Disruption of Hypernetworks via Spectral Partitioning
For researchers studying contagion on hypergraphs, this work provides a targeted hyperedge removal strategy but shows that its performance varies by topology, highlighting the need for further investigation.
The authors propose a spectral partitioning method to identify hyperedges for removal to suppress contagion on hypergraphs, but find that its effectiveness is topology-dependent, outperforming random removal only for Erdős–Rényi hypergraphs, while being comparable or worse for Watts–Strogatz and Barabási–Albert hypergraphs.
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.