Emergence of temporal higher-order interactions from pairwise collaboration

Temporal higher-order networks capture the evolving multi-body interactions in complex systems. Conventional generative models typically prescribe birth-death rules for each higher-order interaction, but the intrinsic mechanism leading to the emergence of higher-order interactions remains to be investigated. In this paper, we introduce a Pairwise-Induced Temporal Higher-Order Network model (PITHON), in which the spontaneous emergence of higher-order interactions can be traced back to the microscopic pairwise collaboration. In combination with empirical data, it is demonstrated that PITHON is able to reproduce primary characters of real-world systems, including activity levels, interaction durations, temporal-topological correlations, and cross-order evolution patterns. PITHON offers a plausible explanation to the origin of temporal higher-order interactions in certain real systems such as face-to-face interaction. Additionally, it can produce high-quality data of temporal higher-order networks with flexibility and efficiency, which supports further studies on dynamical processes as well as deep learning approaches. Temporal higher-order interactions are prevalent in real systems, yet the underlying mechanisms remain underexplored. This article provides a potential explanation for the spontaneous emergence of such interactions, by considering collaborative effects between pairwise interactions.