A Generative Hypergraph Model for Double 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.

arXiv comment11 pages, 6 figures

References in corpus (23)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Power laws, Pareto distributions and Zipf's law
• Mean-field theory for scale-free random networks
• Networks beyond pairwise interactions: structure and dynamics
• Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
• Simplicial models of social contagion
• Evolutionary dynamics of higher-order interactions in social networks
• Dynamics on higher-order networks: A review
• Evolution of reference networks with aging
• Clique topology reveals intrinsic geometric structure in neural correlations
• Random hypergraphs and their applications
• The first-mover advantage in scientific publication
• Rate equation approach for correlations in growing network models
• Hypergraph topological quantities for tagged social networks
• Weighted Growing Simplicial Complexes
• Growing scale-free simplices
• Global topological synchronization on simplicial and cell complexes
• The Aging Effect in Evolving Scientific Citation Networks
• Brand effect versus competitiveness in hypernetworks
• Population stratification using a statistical model on hypergraphs
• Time-invariant degree growth in preferential attachment network models