Hypergraph reconstruction from network data

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.

13 pages, 7 figures. Code is available at https://graph-tool.skewed.de/

References in corpus (5)

• Modularity and community structure in networks
• Cooperative Game Theory Approaches for Network Partitioning
• Structure of large random hypergraphs
• Bayesian inference of network structure from unreliable data
• Preferential attachment of communities: the same principle, but a higher level

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• Hyperlink communities in higher-order networks
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• Persistent Homology of Fractional Gaussian Noise
• Compressing network populations with modal networks reveals structural diversity
• Filtering higher-order datasets
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• Message-Passing on Hypergraphs: Detectability, Phase Transitions and Higher-Order Information
• Higher-order dissimilarity measures for hypergraph comparison
• Higher-order shortest paths in hypergraphs
• Symmetry-driven embedding of networks in hyperbolic space
• Beyond Trivial Edges: A Fractional Approach to Cohesive Subgraph Detection in Hypergraphs
• Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs