超网络模型构建及特性分析  

Hypernetwork Model and Its Properties

作　　者：刘胜久[1,2] 李天瑞[1,2] 洪西进[1,2,3] 王红军[1,2] 珠杰[1,2,4] LIU Shengjiu;LI Tianrui;HORNG Shijinn;WANG Hongjun;ZHU Jie(School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China;Key Lab of Cloud Computing and Intelligent Technique of Sichuan Province, Chengdu 611756, China;Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology,Taipei 10607, China;Department of Computer Science, Tibetan University, Lhasa 850000, China)

机构地区：[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]台湾科技大学资讯工程系,台北10607 [4]西藏大学计算机系,拉萨850000

出　　处：《计算机科学与探索》2017年第2期194-211,共18页Journal of Frontiers of Computer Science and Technology

基　　金：国家自然科学基金Nos.61175047;61262058;61152001;中国科学院自动化研究所复杂系统管理与控制重点实验室开放课题No.20110102~~

摘　　要：关联矩阵是超网络的一种表述形式,节点度、节点超度和超边度是度量超网络的一种方法。从关联矩阵出发对超网络进行研究,重点研究了自相似超网络及随机超网络,并给出了基于矩阵运算的超网络构建方法的若干性质。自相似超网络可通过对一个简单初始超图的关联矩阵进行迭代的Tracy-Singh积运算得到,而随机超网络可通过对多个简单初始超图的关联矩阵进行顺次的Tracy-Singh和运算得到。自相似超网络的分形维数不超过2,且当初始超图是连通的且非二分超图时,自相似超网络的直径不超过初始超图直径的两倍,即同时具有小世界特性。随机超网络的节点度、节点超度和超边度均呈正态分布。仿真实验证实了所构建的超网络的各项特性。Correlation matrix describes hypernetwork briefly and intuitively.Hypernetwork can be characterized bynode degree,node hyperdegree and hyperedge degree.This paper studies hypernetwork especially self-similar hypernetworkand random hypernetwork from the perspective of correlation matrix,and shows several properties ofapproaches for constructing hypernetwork based on matrix operation.Self-similar hypernetwork can be obtained byTracy-Singh product on the correlation matrix of a simple initial hypergraph iteratively,and random hypernetwork canbe obtained by Tracy-Singh sum on the correlation matrixes of multiple simple initial hypergraphs sequentially.The fractal dimension of self-similar hypernetworks is no larger than2.When the initial hypergraph is a connected and nonbipartitehypergraph,the diameter of self-similar hypernetwork does not exceed twice of that of the initial hypergraph,namely,it also shares a small-world property.The distributions of node degrees,node hyperdegrees and hyperedgedegrees of random hypernetworks are normal.The results of simulation experiments validate the properties of the constructedhypernetwork.

关 键 词：超网络 矩阵运算 自相似超网络 分形维数 随机超网络 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]