Hypergraph reconstruction from network data

Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the fundamental interactions involve more than two entities at the same time. Pairwise representations nonetheless remain ubiquitous, because higher-order interactions are often not recorded explicitly in network data. Here, we introduce a Bayesian approach to reconstruct latent higher-order interactions from ordinary pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them. We demonstrate its applicability to a wide range of datasets, both synthetic and empirical. Higher-order interactions intervene in a large variety of networked phenomena, from shared interests known to influence the creation of social ties, to co-location shaping networks embedded in space, like power grids. This work introduces a Bayesian framework to infer higher-order interactions hidden in network data.