Networks can describe the structure of a wide variety of complex systems by specifying how pairs of nodes interact. This choice of representation is flexible, but not necessarily appropriate when joint interactions between groups of nodes are needed to explain empirical phenomena. Networks remain the de facto standard, however, as relational datasets often fail to record higher-order interactions. To address this gap, we here introduce a Bayesian approach to reconstruct the higher-order interactions  from pairwise network data. Our method is based on the principle of parsimony and does not reconstruct higher-order structures when there is scant statistical evidence . We demonstrate that our approach successfully uncovers higher-order interactions in synthetic and empirical network data .
Networks can describe the structure of a wide variety of complex systems by specifying how pairs of nodes interact. This choice of representation is flexible, but not necessarily appropriate when joint interactions between groups of nodes are needed to explain empirical phenomena. Networks remain the de facto standard, however, as relational datasets often fail to include higher-order interactions. Here, we introduce a Bayesian approach to reconstruct these missing higher-order interactions , from 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 .
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