Targeted Disruption of Hypernetworks via Spectral Partitioning

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.