Journal of Computer Applications ›› 2019, Vol. 39 ›› Issue (11): 3107-3113.DOI: 10.11772/j.issn.1001-9081.2019050806

• The 2019 China Conference on Granular Computing and Knowledge Discovery (CGCKD2019) •     Next Articles

Measure method and properties of weighted hypernetwork

LIU Shengjiu1,2, LI Tianrui1,2, YANG Zonglin1,2, ZHU Jie3   

  1. 1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu Sichuan 611756, China;
    2. Sichuan Key Laboratory of Cloud Computing and Intelligent Technique, Chengdu Sichuan 611756, China;
    3. School of Information Science and Technology, Tibet University, Lhasa Tibet 850000, China
  • Received:2019-05-06 Revised:2019-05-22 Online:2019-11-10 Published:2019-09-11
  • Supported by:
    This work is partially supported by the National Natural Science Foundation of China (61262058, 61751216).

带权超网络的度量方法及其性质

刘胜久1,2, 李天瑞1,2, 杨宗霖1,2, 珠杰3   

  1. 1. 西南交通大学 信息科学与技术学院 成都 611756;
    2. 四川省云计算与智能技术高校重点实验室, 成都 611756;
    3. 西藏大学 信息科学技术学院, 拉萨 850000
  • 通讯作者: 李天瑞
  • 作者简介:刘胜久(1988-),男,湖北随州人,博士,主要研究方向:复杂网络、自然语言处理、数据挖掘;李天瑞(1969-),男,福建莆田人,教授,博士,CCF会员,主要研究方向:粗糙集、粒计算、数据挖掘;杨宗霖(1994-),男,福建漳州人,硕士研究生,主要研究方向:自然语言处理、云计算;珠杰(1973-),男,西藏日喀则人,教授,博士,CCF会员,主要研究方向:自然语言处理、数据挖掘。
  • 基金资助:
    国家自然科学基金资助项目(61262058,61751216)。

Abstract: Hypernetwork is a kind of networks which is more complex than the ordinary complex network. Hypernetwork can describe complex system existing in the real world more appropriately than complex network since every hyperedge of it can connect any number of nodes. A new method to measure hypernetwork-Hypernetwork Dimension (HD) was proposed aiming to the shortcomings and deficiencies of existing measure method of hypernetwork. Hypernetwork dimension was expressed as twice as much as the ratio of the logarithm of the sum of all nodes' weights and product of corresponding hyperedge's weight in all hyperedges to the logarithm of the product of sum of hyperedges' weights and sum of nodes' weights. The hypernetwork dimension was able to be applied to the weighted hyperworks with many different numerical types of both nodes' weights and hyperedges' weights, such as positive real numbers, negative real numbers, pure imaginary numbers, and even complex numbers. Finally, several important properties of the proposed hypernetwork dimension were discussed.

Key words: complex network, hypergraph, hypernetwork, Fractal Dimension (FD), Network Dimension (ND), hypernetwork dimension

摘要: 超网络是较通常意义上的复杂网络更为复杂的网络,该网络的每一条超边能连接任意多个节点的特性使其比复杂网络能更好地描述真实世界中的复杂系统。针对现有超网络研究中对超网络度量方法的缺陷与不足,提出了一种超网络度量方法——超网络维数(HD),即为所有超边包含的节点权重之和与对应超边权重乘积和的对数值和节点权重之和与超边权重之和乘积对数值的比值的两倍。超网络维数可以应用于节点权重与超边权重为正实数、负实数、纯虚数,乃至复数等多种不同数值类型的带权超网络中。最后给出了超网络维数的若干性质。

关键词: 复杂网络, 超图, 超网络, 分形维数, 网络维数, 超网络维数

CLC Number: