A Generative Hypergraph Model for Double Heterogeneity

TL;DR

This paper introduces a generative hypergraph model that captures double heterogeneity in network systems by employing preferential attachment, producing scale-free distributions in hyperdegree and hyperedge size, and aligning well with numerical simulations.

Contribution

It presents a novel hypergraph growth model incorporating preferential attachment in both nodes and hyperedges, addressing the gap in linking network growth with hyperedge expansion.

Findings

The model produces scale-free distributions in hyperdegree and hyperedge size.

Mean-field analysis matches numerical simulations.

The model helps understand systems with dual heterogeneity.

Abstract

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect more than two nodes, have thus become a new paradigm in network science. Yet, we are still in lack of models linking network growth and hyperedge expansion, both of which are commonly observable in the real world. Here, we propose a generative hypergraph model by employing the preferential attachment mechanism in both nodes and hyperedge formation. The model can produce bi-heterogeneity, exhibiting scale-free distributions in both hyperdegree and hyperedge size. We provide a mean-field treatment that gives the expression of the two scaling exponents, which agree with the numerical simulations. Our model may help to understand the networked systems showing both types of heterogeneity and facilitate the study of complex dynamics thereon.