Pairwise comparison

Quantum mechanics

Scale (ratio)

Power law

Ecology

Biology

Statistics

Hypergraph

Poisson distribution

Degree (music)

Distribution (mathematics)

Economics

Acoustics

Complex network

Statistical physics

Type (biology)

Physics

Mathematics

Mathematical analysis

Combinatorics

Degree distribution

Finance

Order (exchange)

Journal of Statistical Mechanics Theory and Experiment

The hypergraph offers a platform to study structural properties emerging from more complicated and higher-order than pairwise interactions among constituents and dynamical behavior such as the spread of information or disease. Recently, a simplicial contagion problem was introduced and considered using a simplicial susceptible-infected-susceptible (SIS) model. Although recent studies have investigated random hypergraphs with a Poisson-type facet degree distribution, hypergraphs in the real world can have a power-law type of facet degree distribution. Here, we consider the SIS contagion problem on scale-free uniform hypergraphs and find that a continuous or hybrid epidemic transition occurs when the hub effect is dominant or weak, respectively. We determine the critical exponents analytically and numerically. We discuss the underlying mechanism of the hybrid epidemic transition.

Simplicial SIS model in scale-free uniform hypergraph