Simplicial Closure and higher-order link prediction

Significance Networks provide a powerful abstraction for complex systems throughout the sciences by representing the underlying set of pairwise interactions, but much of the structure within these systems involves interactions that take place among more than two nodes at once. While these higher-order interactions are ubiquitous, an evaluation of the basic properties and organizational principles in such systems is missing. Here we study 19 datasets from biology, medicine, social networks, and the web and characterize how higher-order structure emerges and differs between domains. We then propose a general framework for evaluating higher-order data models based on link prediction, a task in which we seek to predict future interactions from a system’s structure and past history. 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 difference from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.