Year: 2025
Type: article
Abstract: Complex networks play a crucial role in the study of collective behavior, encompassing the analysis of dynamical properties and network topology. In real-world systems, higher-order interactions among multiple entities are widespread and significantly influence collective dynamics. Here, we extend the synchronization alignment function framework to hypergraphs of arbitrary order by leveraging the multi-order Laplacian matrix to encode higher-order interactions. Our findings reveal that the upper bound of synchronous behavior is determined by the maximum eigenvalue of the multi-order Laplacian matrix. Furthermore, we decompose the contribution of each hyperedge to this eigenvalue and utilize it as a basis for designing an eigenvalue-based topology modification algorithm. This algorithm effectively enhances the upper bound of synchronous behavior without altering the total number of higher-order interactions. Our study provides new insights into dynamical optimization and topology tuning in hypergraphs, advancing the understanding of the interplay between higher-order interactions and collective dynamics.
Source: Chinese Physics B
Authors: Chong-Yang 重阳 Wang 王, Bi-Yun 碧芸 Ji 季, Linyuan 琳媛 Lü 吕
Institution: University of Science and Technology of China
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4409550817