title: Non-uniform Evolving Hypergraphs and Weighted Evolving Hypergraphs.
abstract: Firstly, this paper proposes a non-uniform evolving hypergraph model with nonlinear preferential attachment and an attractiveness. This model allows nodes to arrive in batches according to a Poisson process and to form hyperedges with existing batches of nodes. Both the number of arriving nodes and that of chosen existing nodes are random variables so that the size of each hyperedge is non-uniform. This paper establishes the characteristic equation of hyperdegrees, calculates changes in the hyperdegree of each node, and obtains the stationary average hyperdegree distribution of the model by employing the Poisson process theory and the characteristic equation. Secondly, this paper constructs a model for weighted evolving hypergraphs that couples the establishment of new hyperedges, nodes and the dynamical evolution of the weights. Furthermore, what is obtained are respectively the stationary average hyperdegree and hyperstrength distributions by using the hyperdegree distribution of the established unweighted model above so that the weighted evolving hypergraph exhibits a scale-free behavior for both hyperdegree and hyperstrength distributions.
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai 200093, PR China.
authors.forename: Jin-Li
authors.initials: JL
authors.lastname: Guo
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai 200093, PR China.
authors.forename: Xin-Yun
authors.initials: XY
authors.lastname: Zhu
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai 200093, PR China.
authors.forename: Qi
authors.initials: Q
authors.lastname: Suo
authors.affiliation: School of Business, Slippery Rock University, Slippery Rock, PA 16057, USA.
authors.forename: Jeffrey
authors.initials: J
authors.lastname: Forrest