Simplicial Closure and higher-order link prediction

TL;DR

This paper investigates the structure and evolution of higher-order interactions in complex networks, revealing consistent patterns across datasets and proposing higher-order link prediction as a new benchmark for modeling such interactions.

Contribution

It introduces the study of higher-order interactions in temporal networks, analyzes their organizational principles, and proposes higher-order link prediction as a novel benchmark problem.

Findings

Higher-order interactions show consistent patterns across similar system types.

Tie strength and edge density are key indicators of higher-order organization.

Local information is more important than long-range information in predicting new higher-order interactions.

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.