带权超网络的多重分形研究

doi:10.3969/j.issn.0253-2778.2020.03.016

中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (3): 369-381.DOI: 10.3969/j.issn.0253-2778.2020.03.016

带权超网络的多重分形研究

刘胜久，李天瑞，刘佳，谢鹏

1.西南交通大学信息科学与技术学院，四川成都 611756；2.四川省云计算与智能技术高校重点实验室，四川成都 611756

收稿日期:2019-07-15 修回日期:2019-09-28 接受日期:2019-09-28 出版日期:2020-03-31 发布日期:2019-09-28
通讯作者: 李天瑞
作者简介:刘胜久，男，1988年生，博士.研究方向：数据挖掘、复杂网络、自然语言处理. E-mail: liushengjiu2008@163.com
基金资助:
国家自然科学基金（61573292）资助.

Research on multi-fractals of weighted hypernetworks

LIU Shengjiu, LI Tianrui, LIU Jia, XIE Peng

1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China; 2. Sichuan Key Lab of Cloud Computing and Intelligent Technique, Chengdu 611756, China

Received:2019-07-15 Revised:2019-09-28 Accepted:2019-09-28 Online:2020-03-31 Published:2019-09-28

摘要/Abstract

摘要： 超网络是较通常意义上的复杂网络更为复杂的网络，超网络维数是度量超网络的一种可行的方法．针对带权超网络中节点权重及超边权重可以分别为正实数、负实数、纯虚数及复数等多种不同的类型，首先给出了各种不同类型带权超网络的多重分形维数；然后讨论了带权超网络的多重分形特性；研究表明，在不同类型的带权超网络中，除节点权重及超边权重均为正实数及负实数的两种情形之外，其他类型的带权超网络均具有多重分形特性，且可以分为7个不同的类别，均分布于整个复平面；最后给出了所有这些带权超网络多重分形维数的解析表达式，并分析了这些带权超网络多重分形维数的若干重要性质．

关键词: 超图, 超网络, 超网络维数, 分形理论, 分形维数, 多重分形

Abstract: Hypernetwork is a kind of network that is more complex than ordinary complex networks, while hypernetwork dimension is a feasible tool for measuring it. For the case that both node weight and hyperedge weight in weighted hypernetworks can value among positive real number, negative real number, pure imaginary number and complex number, etc., fractal dimensions for various weighted hypernetworks is proposed and their multi-fractals are discussed. It is shown that among all types of weighted hypernetworks, except those with both node weight and hyperedge weight being positive or negative real numbers, other types of weighted hypernetworks share multi-fractals and can be divided into seven different categories that are all distributed in the entire complex plane. The analytic expressions of multi-fractal dimensions for all types of weighted hypernetworks are also presented. Finally, some important properties of the multi-fractal dimensions of these weighted hypernetworks are analyzed.

Key words: hypergraph, hypernetwork, hypernetwork dimension, fractal theory, fractal dimension, multi-fractals

中图分类号:

TP393

刘胜久，李天瑞，刘佳，谢鹏. 带权超网络的多重分形研究[J]. 中国科学技术大学学报, 2020, 50(3): 369-381.

LIU Shengjiu, LI Tianrui, LIU Jia, XIE Peng. Research on multi-fractals of weighted hypernetworks[J]. Journal of University of Science and Technology of China, 2020, 50(3): 369-381.

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带权超网络的多重分形研究

Research on multi-fractals of weighted hypernetworks

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