Eigenvector localization in hypergraphs: Pairwise versus higher-order links

Localization behaviors of Laplacian eigenvectors of complex networks furnish an explanation to various dynamical phenomena of the corresponding complex systems. We numerically examine roles of higher-order and pairwise links in driving eigenvector localization of hypergraphs Laplacians. We find that pairwise interac-tions can engender localization of eigenvectors corresponding to small eigenvalues for some cases, whereas higher-order interactions, even being much much less than the pairwise links, keep steering localization of the eigenvectors corresponding to larger eigenvalues for all the cases considered here. These results will be advantageous to comprehend dynamical phenomena, such as diffusion, and random walks on a range of real-world complex systems having higher-order interactions in better manner.

Automated summary

Localization behaviors of Laplacian eigenvectors of complex networks provide explanations for various dynamical phenomena of corresponding complex systems. Through numerical examination, we find that higher-order interactions, even though much fewer than pairwise links, play a key role in steering localization of eigenvectors corresponding to larger eigenvalues. These findings are beneficial for understanding dynamic phenomena in real-world complex systems with higher-order interactions, such as diffusion and random walks.