一种基于矩阵运算的超网络模型

Shengjiu Liu, Tianrui Li
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引用次数: 3

摘要

本文提出了一种基于Tracy-Singh积的超图关联矩阵超网络模型。引入节点度、节点超度、超边度及其对应的多项式来描述该超网络模型。证明了这种超网络是分形的,因为它的相关矩阵是分形矩阵。给出了分形参数。而且,这种超网络也是小世界的,因为其直径不会超过原始超图直径的两倍。通过一种新颖的节点度多项式、节点超度多项式和超边多项式的乘积,得到节点度、节点超度和超边度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A New Hypernetwork Model Based on Matrix Operation
In this paper, we propose a new hypernetwork model based on Tracy-Singh Product on the correlation matrix of hypergraph. Node degree, node hyperdegree, and hyperedge degree and their corresponding polynomials are introduced to describe this hypernetwork model. It is shown that this kind of hypernetworks is fractal as its correlation matrix is a fractal matrix. The fractal parameter is then given. What's more, this kind of hypernetworks is also small-world for the diameter won't exceed twice the diameter of primitive hypergraph. By a novel product of node degree polynomial, node hyperdegree polynomial and hyperedge degree polynomial, node degree, node hyperdegree and hyperedge degree are obtained.
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