超网络模型构建及特性分析

发布时间：2018-04-03 02:30

本文选题：超网络　切入点：矩阵运算　出处：《计算机科学与探索》2017年02期

【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。
[Abstract]:The incidence matrix is a kind of expression of supernetwork. Node degree, node oversize and super-edge degree are one of the methods to measure supernetwork.Based on the correlation matrix, the supernetwork is studied, and the self-similar supernetwork and the random supernetwork are studied, and some properties of the supernetwork construction method based on matrix operation are given.The self-similar supernetwork can be obtained by iterating the Tracy-Singh product of the correlation matrix of a simple initial hypergraph, while the random supernetwork can be obtained by the sequential Tracy-Singh summation of the correlation matrix of several simple initial hypergraphs.The fractal dimension of the self-similar supernetwork is not more than 2, and when the initial hypergraph is connected and non-bipartite hypergraph, the diameter of the self-similar supernetwork is not more than two times of the initial hypergraph diameter, that is, the self-similar supernetwork has the small-world characteristic at the same time.The node degree, node overpass degree and excess edge degree of random supernetwork are all normal distribution.The simulation results confirm the characteristics of the supernetwork.
【作者单位】：西南交通大学信息科学与技术学院;四川省云计算与智能技术高校重点实验室;台湾科技大学资讯工程系;西藏大学计算机系;
【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~~
【分类号】：O157.5

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