华东师范大学学报（自然科学版） >

2022 , Vol. 2022 >Issue 4: 147 - 153

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.04.015

物理学与电子学

复杂网络度演化的涨落特征

  • 刘琪琛 ,
  • 钱江海 ,
  • 常瀚云
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  • 1. 上海电力大学 数理学院, 上海　200090
    2. 华东师范大学 软硬件协同设计技术与应用教育部工程研究中心, 上海　200062

收稿日期: 2021-08-13

  网络出版日期: 2022-07-19

基金资助

华东师范大学软硬件协同设计技术与应用教育部工程研究中心开放研究基金 (OP202102)

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Fluctuation behavior of the evolution of complex networks

  • Qichen LIU ,
  • Jianghai QIAN ,
  • Hanyun CHANG
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  • 1. College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai　200090, China
    2. Engineering Research Center of Software/Hardware Co-design Technology and Application of the Ministry of Education, East China Normal University, Shanghai　200062, China

Received date: 2021-08-13

  Online published: 2022-07-19

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摘要

复杂网络的发展催生了大量模型以揭示系统的演化规律和结构形成, 但它们在描述度增长的涨落上却存在明显的差异. 为确定哪一类模型更适用于真实系统, 对2个真实网络开展了实证研究. 结果表明, 真实网络中度增长率的涨落不同于任何一类模型的预言, 其涨落指数随观测间隔线性递减, 呈现明显的间隔依赖性; 通过比较源数据与重排连边操作后的涨落行为的变化, 可推断出这种依赖性源于系统内关联效应的增强. 这些结果不仅指出了现有模型的局限, 更揭示了关联性自身的动力学性质, 这对深入理解复杂网络的演化机制有重要意义.

关键词： 度增长; 涨落; 吉布拉定律; 相关性

本文引用格式

刘琪琛 , 钱江海 , 常瀚云 . 复杂网络度演化的涨落特征[J]. 华东师范大学学报（自然科学版）, 2022 , 2022(4) : 147 -153 . DOI: 10.3969/j.issn.1000-5641.2022.04.015

Abstract

Research on complex networks has given birth to models for understanding evolution dynamics and structure formation; their respective degree growth fluctuations, however, behave very differently. To test the validity of existing models, we carry out an empirical study on two real networks. The results show that both their fluctuation exponents decrease linearly with the observation interval, presenting an interval-dependent picture that has not been predicted by any of the existing models. By exploring the response of the fluctuation to shuffling data, we deduce the interval dependence from the reinforcement of the internal temporal correlation. These results reveal not only the limitations of the existing models, but the complex dynamics of the correlation itself, which is significant for further understanding the underlying mechanism of network evolution.

Key words： degree growth; fluctuation; Gibrat’s law; correlation

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