Abstract
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.
Highlights
Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected
If we need the higher-order interactions to give an appropriate description of the social dynamics at play[12], what should we do with such inadequate survey data? As we show in Fig. 1, there are many kinds of higher-order interactions that are compatible with the same network data
We show that the method can find compact descriptions of many empirical networked systems by using latent higher-order interactions, thereby demonstrating that such interactions are in complex systems
Summary
Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. 1234567890():,; Empirical networks are often locally dense and globally sparse[1] Whether they are social, biological, or technological[2], they comprise large groups of densely interconnected nodes, even when only a small fraction of all possible connections exist. If we assume that most ties are created within contexts of limited scopes, the resulting networks are locally dense, matching empirical observations[1,9,10] Despite their tremendous explanatory power, higher-order interactions are seldom used directly to model empirical systems, due to a lack of data[7]. While the context is directly observable for some systems—say, co-authored papers or colocating species—it is unavailable for several others, including brain data[11], typical social interaction data[12], and ecological competitor data[13] to name only a few
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