Functional reducibility of higher-order networks
arxiv(2024)
Abstract
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
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