超网络中标度律的涌现

本文构建超网络和复杂网络中统一演化模型,研究超网络无标度特性演化机理和拓扑性质.利用Poisson过程理论和连续化方法对模型进行分析,获得网络稳态平均超度分布的解析表达式.仿真实验和理论分析相符合.结果表明:随着网络规模的增大,这个动态演化网络的超度分布遵循无标度的特性.它不仅将每次增加一个新节点与若干个老节点围成一条超边的超网络模型和每次增加若干个新节点与一个老节点围成一条超边的超网络模型统一在一个模型中,而且将复杂网络中著名的无标度模型也作为我们模型的特例.

Emergence of scaling in hypernetworks

This paper proposes a unified model for hypernetworks and complex networks, and studies the evolution mechanisms of scale-free hypernetworks and the topological properties of the hypernetwork. We have analyzed the proposed model and calculated the stationary average hyperdegree distribution of the hypernetwork by using a Poisson process theory and a continuous technique. The analytical result agrees well with the simulation. It is shown that the hyperdegree distribution of the dynamic model follows a scale-free law. This paper not only integrates the hypernetwork model, in which one new node forms an edge with some old nodes, and the hypernetwork model, in which some new nodes form an edge with one old node, but also integrates the scale-free model in complex networks.
Keywords： complex network hypergraph hypernetwork scale-free