加权超网络
Weighted Hypernetworks
摘要：
复杂网络理论已被用于研究复杂系统。然而，许多现实生活中的系统涉及多种对象。它们不能用简单的图表来描述。为了提供这些系统的完整信息，我们将复杂网络演化模型的概念扩展到超网络。在本文中，我们首先提出了一个具有吸引力的非均匀超网络模型，并得到了该非均匀超网络的平稳平均超度分布。此外，我们建立了一个加权超网络模型，该模型耦合了新的超边和节点的建立以及权值的动态演化。利用具有吸引力的超网络模型的超度分布，分别得到了该模型的平稳平均超度分布和平稳平均超强分布。特别是，该模型产生了一个非平凡的时间演化节点的属性和无标度行为的超度和超强分布。希望我们的工作能对现实系统中超网络的研究有所帮助。
英文摘要：
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we extend the concept of evolving models of complex networks to hypernetworks. In this work, we firstly propose a non-uniform hypernetwork model with attractiveness, and obtain the stationary average hyperdegree distribution of the non-uniform hypernetwork. Furthermore, we develop a model for weighted hypernetworks that couples the establishment of new hyperedges and nodes and the weights' dynamical evolution. We obtain the stationary average hyperdegree and hyperstrength distribution by using the hyperdegree distribution of the hypernetwork model with attractiveness, respectively. In particular, the model yields a nontrivial time evolution of nodes' properties and scale-free behavior for the hyperdegree and hyperstrength distribution. It is expected that our work may give help to the study of the hypernetworks in real-world systems.
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