Abstract

超网络是描述真实世界事物间日趋复杂关系的最一般且无约束的数学模型,其无标度特性是重要的研究内容.超网络无标度特性的研究基础是超度的分布特征,但是超度的定义是着眼于单个节点的.为了探究超网络中广泛存在的群体的特性从而更充分地发掘超网络表示复杂系统的结构优势,本文扩展了超网络中超度和超度分布的概念.在提出的紧密相关集概念的基础之上,给出了组度的定义,进而提出了组度分布的定义.在两个不同的超网络上研究的结果表明,超网络的组度分布呈现出多样的分布特性.本文的研究结果可以充实超图理论的内容,对超网络中群体特性的研究具有借鉴意义,同时也有利于拓宽网络科学的应用范围.

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