Abstract

A hypergraph is useful to express the relationship between two or more nodes. Real hypergraph data are typically weighted. We propose a weighted evolving hypergraph model that considers preferential attachment. The model allows variability on the two basic components of the evolving hypergraph: the number and the size of the hyperedges to be connected. Under the mild distributional conditions on the two varying quantities, we derive the exact degree distribution that asymptotically follows a power-law distribution. We find that the limiting power-law exponent is affected by the distribution of hyperedge sizes. The distribution of the number of hyperedges to be connected has a considerable impact on a small-degree range in which non-power-law behavior is frequently observed in real data. Moreover, we argue that the degree distribution of the model can be expressed as a mixture of the degree distributions with a fixed number of hyperedges to be connected. The validity and usefulness of the model are explained with interpretations via simulation study and real data analysis.