2023/04/14 by Emilio Cruciani, Cruciani, Emilio, Emanuela L. Giacomelli +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Machine Learning (cs.LG) #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.2304.07203
openalex publication_date 2023/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Complex networked systems in fields such as physics, biology, and social sciences often involve interactions that extend beyond simple pairwise ones. Hypergraphs serve as powerful modeling tools for describing and analyzing the intricate behaviors of systems with multi-body interactions. Herein, we investigate a discrete-time nonlinear averaging dynamics with three-body interactions: an underlying hypergraph, comprising triples as hyperedges, delineates the structure of these interactions, while the vertices update their states through a weighted, state-dependent average of neighboring pairs' states. This dynamics captures reinforcing group effects, such as peer pressure, and exhibits higher-order dynamical effects resulting from a complex interplay between initial states, hypergraph topology, and nonlinearity of the update. Differently from linear averaging dynamics on graphs with two-body interactions, this model does not converge to the average of the initial states but rather induces a shift. By assuming random initial states and by making some regularity and density assumptions on the hypergraph, we prove that the dynamics converges to a multiplicatively-shifted average of the initial states, with high probability. We further characterize the shift as a function of two parameters describing the initial state and interaction strength, as well as the convergence time as a function of the hypergraph structure.