华东师范大学学报(自然科学版) ›› 2017, Vol. 2017 ›› Issue (2): 75-80.doi: 10.3969/j.issn.1000-5641.2017.02.010

• 物理学与电子学 • 上一篇    下一篇

可视图复杂网络度分布拟合比较研究

张蓉, 邹勇   

  1. 华东师范大学 物理与材料科学学院, 上海 200241
  • 收稿日期:2016-03-18 出版日期:2017-03-25 发布日期:2017-03-23
  • 通讯作者: 邹勇,男,副教授,硕士生导师,研究方向为复杂网络结构与动力学.E-mail:yzou@phy.ecnu.edu.cn E-mail:yzou@phy.ecnu.edu.cn
  • 作者简介:张蓉,女,硕士研究生,研究方向为非线性与复杂网络学.E-mail:sandy58756071@sina.com
  • 基金资助:

    国家自然科学基金(11305062)

Comparative regression analysis to degree distributions of visibility graph

ZHANG Rong, ZOU Yong   

  1. School of Physics and Materials Science, East China Normal University, Shanghai 200241, China
  • Received:2016-03-18 Online:2017-03-25 Published:2017-03-23

摘要:

可视图(Visibility Graph,VG)算法为研究时间序列的动力学特性提供了复杂网络的思想.网络的度分布反映了时间序列的动力学特征.通过自回归随机过程和分数布朗运动两种不同数据,分别构建可视图.对比结果表明,在自回归随机过程中,度分布可以用指数函数刻画;而在分数布朗运动中,度分布用幂律函数刻画更为合适.这一结论不但适用于VG算法,同时也适用于水平可视图(Horizontal Visibility Graph,HVG)算法.

关键词: 可视图, 自回归随机过程, 分数布朗运动, 拟合优度

Abstract:

Visibility graph has provided much insight to study the dynamics of time series from the perspective complex network. We construct visibility graphs for time series from both auto-regressive stochastic and fractional Brownian motions. Our results suggest that degree distributions of the resulted complex networks of auto-regressive processes are characterized by exponential forms, while that of fractional Brownian motions obey power-law forms. Our conclusions hold for both the traditional visibility graph and its variant horizontal visibility graph.

Key words: visibility graph, autoregressive stochastic process, fractional Brownian motion, goodness of fit

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