计算机科学与探索 ›› 2021, Vol. 15 ›› Issue (4): 682-689.DOI: 10.3778/j.issn.1673-9418.2006065

• 网络与信息安全 • 上一篇    下一篇

超网络能量研究与应用

刘胜久,李天瑞,刘佳,谢鹏   

  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
  • 出版日期:2021-04-01 发布日期:2021-04-02

Research and Application of Hypernetwork Energy

LIU Shengjiu, LI Tianrui, LIU Jia, XIE Peng   

  1. 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
  • Online:2021-04-01 Published:2021-04-02

摘要:

图能量是图论研究的重要内容,图能量及其变种已在无向图、有向图、混合图等其他多种类型的图中得到很多成功的应用。超网络是一类较传统意义上的复杂网络更为复杂的网络。大多数图能量均是基于矩阵特征值计算得到的,无法推广应用到超网络中,应用范围受限。基于网络维数的网络能量已先后应用于无向图、有向图等多种类型图的分析研究中,并与无向图的图能量及有向图的斜能量等其他类似能量之间存在密切关联。基于超网络的超网络维数,结合网络能量,将超网络维数应用于超网络中,提出了超网络的超网络能量,给出了超网络能量的若干上下限,论证了超网络的超网络能量与图的网络能量之间的内在关联,最后分析了超网络的超网络能量若干重要性质。

关键词: 复杂网络, 超网络, 图能量, 网络能量, 超网络能量

Abstract:

Graph energy plays an important role in research of graph theory. Graph energy and many other similar variants have been applied in many other types of graphs, e.g., undirected graphs, oriented graphs, mixed graphs, and so on. Hypernetwork is a kind of network which is more complex than traditional complex network. Most graph energies are calculated based on the eigenvalues of matrix and can hardly be extended to hypernetwork, which limits their application range. Network energy based on network dimension has been applied in undirected graphs and oriented graphs one by one, and is closely related to many other energy-like quantities, e.g., graph energy of undirected graphs, skew energy of oriented graphs, and so on. In this paper, based on hypernetwork dimension of hypernetwork and combined with network energy, hypernetwork energy of hypernetwork is proposed with application of hypernetwork dimension on hypernetwork. At the same time, several upper and lower limits of hypernetwork energy are given, and the internal relations between hypernetwork energy of hypernetwork and network energy of graphs are demonstrated. Finally, several important properties of hypernetwork energy are analyzed as well.

Key words: complex network, hypernetwork, graph energy, network energy, hypernetwork energy