基于节点加权和边加权的重分形研究  

Multifractal Research Based on Node-Weight and Edge-Weight

作　　者：母金鸣 MU Jinming(Key Laboratory of Cognitive Radio and Information Processing,Ministry of Education,Guilin University of Electronic Technology,Guilin 541004)

机构地区：[1]桂林电子科技大学认知无线电与信息处理教育部重点实验室,桂林541004

出　　处：《计算机与数字工程》2021年第3期521-524,共4页Computer & Digital Engineering

基　　金：国家自然科学基金项目(编号:61561014,61761014);认知无线电与信息处理教育部重点实验室(编号:CRKL170106);广西研究生教育创新计划项目(编号:YCBZ2017050)资助。

摘　　要：目前对于网络重分形的研究,在网络权重性质方面主要是原始网络、节点加权网络、边加权网络,每一个都是单独进行研究,论文主要对同时包含节点权重和边权重的网络进行分析,研究网络广义分形维数的变化情况。首先对已有的沙箱算法进行改进,并利用分形布朗运动时间序列进行改进算法的验证,然后利用改进的沙箱算法对由分形布朗运动时间序列生成的同时包含节点权重和边权重的可视复杂网络进行计算,接着同时单独改变边权重和节点权重,进一步研究广义分形维数随边权重和节点权重改变的变化情况。结果表明改进沙箱算法在保持了传统沙箱算法计算精度的前提下,大大地提高了计算的速度。对于同时单独改变节点权重和边权重,对复杂网络的广义分形维数的影响是截然不同的,节点权重的变化基本不影响网络广义分形维数的变化,而边权重则大大的影响且不同权重指数下的影响情况各不相同。At present,the research on network multifractal mainly focuses on the original network,node-weighted network and edge-weighted network,each of which is studied separately.This paper mainly analyses the network which contains both node weight and edge weight,and finds out the change of the generalized fractal dimension of the network.Firstly,the existing sandbox algorithm is improved,and the improved algorithm is validated by using fractal Brownian motion time series.Then,the improved sandbox algorithm is used to calculate the visual complex network generated by fractal Brownian motion time series,which contains both node weight and edge weight.Then,the edge weight and node weight are changed separately,and the generalized fractal di⁃mension is further studied.With the change of edge weight and node weight,the results show that the improved sandbox algorithm greatly improves the calculation speed while maintaining the accuracy of the traditional sandbox algorithm.For changing node weight and edge weight separately at the same time,the influence on the generalized fractal dimension of complex networks is quite differ⁃ent.The change of node weight basically does not affect the change of the generalized fractal dimension of networks,while the influ⁃ence of edge weight is great and different under different weight index.

关 键 词：分形布朗运动 广义分形维数 边权重 节点权重 

分 类 号：O157.5[理学—数学]