Simplicial closure and higher-order link prediction

TLDR

Networks model complex systems via pairwise interactions, yet many systems involve higher‑order interactions among groups of nodes, which are ubiquitous but understudied, leaving organizational principles largely unknown. The study aims to analyze the temporal evolution of 19 datasets with higher‑order interactions and to establish higher‑order link prediction as a benchmark. The authors analyze 19 datasets, explicitly accounting for higher‑order interactions, and propose a benchmark problem for predicting higher‑order links. The datasets exhibit rich higher‑order structure with consistent patterns across system types, tie strength and edge density act as competing positive indicators of higher‑order organization, and higher‑order link prediction relies more on local than long‑range information compared to pairwise link prediction.

Abstract

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.