Randomizing hypergraphs preserving degree correlation and local clustering

TL;DR

This paper introduces the hyper dK-series, a family of randomized hypergraph models that preserve key structural properties, enabling better analysis of higher-order interactions in complex systems.

Contribution

It extends the dK-series framework to hypergraphs, allowing preservation of degree, degree correlation, redundancy, and hyperedge size in randomized models.

Findings

Hyper dK-series effectively preserves targeted hypergraph properties.

Application to epidemic spreading shows impact of higher-order structure.

Application to evolutionary games demonstrates the model's utility.

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.