Group interactions

Empirical complex systems are widely assumed to be characterized not only by pairwise interactions, but also by higher-order (group) interactions that affect collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks’ superior descriptive power – compared to classical pairwise networks – comes with a much increased model complexity and computational cost. Consequently, it is of paramount importance to establish a quantitative method to determine when such a modeling framework is advantageous with respect to pairwise models, and to which extent it provides a parsimonious description of empirical systems. Here, we propose a principled method, based on information compression, to analyze the reducibility of higher-order networks to lower-order interactions, by identifying redundancies in diffusion processes while preserving the relevant functional information. The analysis of a broad spectrum of empirical systems shows that, although some networks contain non-compressible group interactions, others can be effectively approximated by lower-order interactions – some technological and biological systems even just by pairwise interactions. More generally, our findings mark a significant step towards minimizing the dimensionality of models for complex systems

We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based on diffusion dynamics was recently introduced for complex networks with dyadic interactions. Despite mounting evidence of the importance of polyadic interactions, we still lack a general RG scheme for higher-order networks. Our approach uses a diffusion process to group nodes or simplices, where information can flow between nodes and between simplices (higher-order interactions). This approach allows us (i) to probe higher-order structures, defining scale-invariance at various orders, and (ii) to propose a coarse-graining scheme. We demonstrate our approach on controlled synthetic higher-order systems and then use it to detect the presence of order-specific scale-invariant profiles of real-world complex systems from multiple domains.

The interplay between causal mechanisms and emerging collective behaviors is a central aspect of the understanding, control, and prediction of complex networked systems. Here we study this interplay in the context of higher-order mechanisms and behaviors in two representative models: a simplicial Ising model and a simplicial social contagion model. In both systems, we find that group (higher-order) interactions show emergent synergistic (higher-order) behavior. The emergent synergy appears only at the group level and depends in a complex non-linear way on the tradeoff between the strengths of the low- and higher-order mechanisms, and is invisible to low-order behavioral observables. Finally, we present a simple method to detect higher-order mechanisms by using this signature.

Traditional models of human brain activity often represent it as a network of pairwise interactions between brain regions. Going beyond this limitation, recent approaches have been proposed to infer higher-order interactions from temporal brain signals involving three or more regions. However, to this day it remains unclear whether methods based on inferred higher-order interactions outperform traditional pairwise ones for the analysis of fMRI data. To address this question, we conducted a comprehensive analysis using fMRI time series of 100 unrelated subjects from the Human Connectome Project. We show that higher-order approaches greatly enhance our ability to decode dynamically between various tasks, to improve the individual identification of unimodal and transmodal functional subsystems, and to strengthen significantly the associations between brain activity and behavior. Overall, our approach sheds new light on the higher-order organization of fMRI time series, improving the characterization of dynamic group dependencies in rest and tasks, and revealing a vast space of unexplored structures within human functional brain data, which may remain hidden when using traditional pairwise approaches.