Search for: All records

Networks provide a powerful formalism for modeling complex sys- tems, by representing the underlying set of pairwise interactions. But much of the structure within these systems involves interac- tions 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 co-authors, or biological interaction between a set of molecules rather than just two. We refer to these type of simultaneous interactions on sets of more than two nodes as higher-order interactions; they are ubiquitous, but the empirical study of them has lacked a general framework for evaluating higher-order models. Here we introduce such a framework, based on link prediction, a fundamental prob- lem in network analysis. The traditional link prediction problem seeks to predict the appearance of new links in a network, and here we adapt it to predict which (larger) sets of elements will have fu- ture interactions. We study the temporal evolution of 19 datasets from a variety of domains, and use our higher-order formulation of link prediction to assess the types of structural features that are most predictive of new multi-way interactions. Among our results, we find that different domains vary considerably in their distri- bution of higher-order structural parameters, and that the higher- order link prediction problem exhibits some fundamental differ- ences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the ap- pearance of new interactions.