Randomizing hypergraphs preserving degree correlation and local clustering

Abstract

Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics of given hypergraphs, a solid practice is to compare them with those for randomized hypergraphs that preserve some specific properties of the original hypergraphs. In the present study, we propose a family of such reference models for hypergraphs, called the hyper dK-series, by extending the so-called dK-series for dyadic networks to the case of hypergraphs. The hyper dK-series preserves up to the individual node's degree, node's degree correlation, node's redundancy coefficient, and/or the hyperedge's size depending on the parameter values. We also apply the hyper dK-series to numerical simulations of epidemic spreading and evolutionary game dynamics on empirical hypergraphs.

28 pages, 9 figures, 10 tables. Our code is available at "https://github.com/kazuibasou/hyper-dk-series"

References in corpus (6)

• Modularity and community structure in networks
• Random graphs with clustering
• Random graphs containing arbitrary distributions of subgraphs
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• Simplicial SIS model in scale-free uniform hypergraph
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Cited by in corpus (8)

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• Random Recursive Hypergraphs
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• Entropy-based models to randomize real-world hypergraphs
• Attributed Hypergraph Generation with Realistic Interplay Between Structure and Attributes
• Higher-order shortest paths in hypergraphs
• Higher-order null models as a lens for social systems
• Sampling nodes and hyperedges via random walks on large hypergraphs