Higher order versus pairwise interactions: A modeling debate

In recent years, network and complexity science has seen a massive surge in models using hypergraphs and simplicial complexes to represent higher-order interactions (HOIs). These frameworks are built on the premise that pairwise links (standard graphs) could be fundamentally insufficient to capture group dynamics such as social contagion and multi-body synchronization. But it is not always clear what is exactly meant by a HOI: Does it correspond to a genuine group interaction, encoded by an explicit three-body or higher-order potential, or can it emerge from combinations of pairwise interactions? Under what conditions can HOI interactions be reduced to effective dyadic interactions? How is an hyperedge representation reflected in a macroscopic description? When is a hypergraph representation needed to describe empirical data?These questions and the broad and rapid adoption of hypergraph representations have sparked a profound modeling debate. Recent work questions whether many proposed higher-order phenomena are mathematically reducible to pairwise interactions. Skeptics argue that higher-order representations may introduce unnecessary parameter complexity without offering new physical or structural insights, while proponents maintain that simplicial and hypergraph models capture essential, non-reducible dynamics.The goal of this Research Topic is to host a peer-reviewed modeling debate on the necessity, usefulness, and reducibility of higher-order interactions in complex systems. Rather than compiling standard applications of hypergraphs, this collection aims to bring together contrasting viewpoints to critically evaluate when and why higher-order frameworks are scientifically justified. We seek to establish rigorous modeling standards, define the boundaries of pairwise representations, and clarify the significance of multi-body interactions.We welcome contributions that address the mathematical, physical, and computational limits of higher-order models compared to pairwise frameworks. We encourage authors to submit both theoretical papers and empirical validations. To foster a lively, constructive debate, we actively welcome short-format articles (Perspectives, Opinions, and Commentaries) from key voices in the community.Key areas of interest include, but are not limited to:o Mathematical and information-theoretic reducibility of hypergraphs and simplicial complexes to pairwise structures.o Critical evaluations of the expressiveness of graphs versus higher-order models in social, biological, ecological and physical systems.o Empirical validation of higher-order dynamics (e.g., simplicial contagion, higher-order synchronization) against rigorous pairwise null models.o Parameter complexity, overfitting, and model selection in hypernetworks.o Conceptual debates on “overselling” versus genuine scientific breakthroughs in network science. Topic editors: Maxi San Miguel Source: https://www.frontiersin.org/research-topics/82910/higher-order-versus-pairwise-interactions-a-modeling-debate