Information-theoretic metrics for higher-order interactions on graphs

Abstract

[eng] In this work, we contribute to the growing understanding of higherorder interactions (those involving more than two variables) in complex networks, in particular the distinction between higher-order mechanisms and higher-order behaviors. We employ the dynamical Oinformation, a newly-developed metric based on information theory, to detect the presence of higher-order behaviors from time-series data. Our work comprises a thorough numerical study of the behavior of this metric under different synthetic dynamics and models for epidemic spreading on small graphs. We find interesting and sometimes surprising dependence on the infection parameters in spreading models and on the strength of the higher-order mechanism. These results help us develop the intuition necessary for applying this methodology to detect higher-order mechanisms in dynamics on complex networks, and in general to study the synergies resulting from network effects. The methods explored in this work have the potential to illuminate our understanding of higher-order interactions, their definition and importance, and to highlight their role in the emergence of complex dynamics in general