Targeted Disruption of Hypernetworks via Spectral Partitioning
Spectral clustering of hyperedge overlaps outperforms random removal only on Erdős–Rényi graphs.
Researchers Bailey, Hasenjager, and Fefferman from the University of Tennessee and Rutgers introduce a novel method to disrupt contagion spread on hypergraphs – networks where edges can connect more than two nodes, capturing complex group interactions like disease clusters or misinformation cascades. Their approach converts hypergraphs into s-line graphs, where each vertex represents a hyperedge and edges encode overlaps of size s. By applying spectral k-way clustering to these s-line graphs, they compute a multiscale 'cut-persistence' score to rank hyperedges for removal, aiming to break contagion pathways efficiently.
Testing on three synthetic hypergraph types derived from classic graph models (Erdős–Rényi, Barabási–Albert, and Watts–Strogatz), the team simulated infection spread and compared their targeted removal to random hyperedge deletion. Results revealed strong topology dependence: in Erdős–Rényi hypergraphs, cut-persistence targeting significantly reduced final infection size. However, on Barabási–Albert and Watts–Strogatz hypergraphs, random removal performed comparably or even better. This suggests that while spectral overlap can identify structurally salient hyperedges, structural salience alone does not guarantee optimal contagion suppression. The study (16 pages, arXiv:2605.02993) calls for further ensemble-level experiments and higher-order contagion models to refine disruption strategies.
- Method uses spectral clustering of s-line graphs to assign cut-persistence scores to hyperedges for targeted removal.
- On Erdős–Rényi hypergraphs, targeted removal reduced infection size more than random removal.
- On Barabási–Albert and Watts–Strogatz hypergraphs, random removal was equally or more effective.
Why It Matters
Network disruption strategies must be tailored to topology – a universal method risks wasted effort on certain structures.