Information-theoretic metrics of higher-order interactions on graphs

In this work, we contribute to the growing understanding of higher-order interactions (those involving more than two variables), in particular the distinction between higher-order mechanisms and higher-order behaviors. We employ 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. The ultimate aim is applying this methodology to identify higher-order mechanisms in dynamics on complex networks, and in general to study the synergies resulting from network effects. To this end, we also present preliminary results on applying this metric on SIS dynamics on small networks. The methods explored in this work have the potential to illuminate our understanding of higher-order interactions, their definition and importance, and thus of the nature of complex systems in general.