Pairwise Network Loops Produce Higher-Order Sync Without Hyperedges

Physicists at Universitat Rovira i Virgili showed in Communications Physics that ordinary pairwise networks can host genuine higher-order dynamical constraints encoded in the geometry of their loops. Their twisted Laplacian has a zero mode only when every cycle holonomy vanishes.

• Study published in Communications Physics by Nature Portfolio
• Cycle holonomy is gauge-invariant and independent of node labeling
• Twisted Laplacian has a zero mode only if all cycle holonomies vanish
• Smallest eigenvalue measures the network's topological frustration