Visibility graph analysis of temporal irreversibility in sleep electroencephalograms

  • Hui XiongEmail author
  • Pengjian Shang
  • Fengzhen Hou
  • Yan Ma
Original Paper


The study of sleep has continued to garner increased attention. However, most studies assume stationarity of sleep electroencephalogram (EEG) signals, whereas they are typically nonlinear and nonstationary. Little work has focused on the time irreversibility of sleep EEG signals. Hence, the aim of this work is to reveal the temporally irreversible structures of rapid-eye-movement (REM) and non-REM sleep using a visibility algorithm, which is robust to nonstationarity and finite-size effect. Results show that the temporal structure of non-REM sleep is more irreversible than that of REM sleep. The degree of irreversibility is highest in slow-wave sleep. Moreover, statistical analysis suggests that aging is the major factor that affects the irreversibility of sleep signals, while gender and body mass index contribute insignificantly. The dominant role of slow oscillations on the irreversible structures of the sleep signals is also indicated.


Visibility graph Time irreversibility EEG Sleep stage Empirical mode decomposition NARMA 



The authors acknowledge the financial support from the Fundamental Research Funds for the Central Universities (2017YJS207) and National Natural Science Foundation of China (61771035). H. Xiong thanks the support of China Scholarship Council (201707090024) during her visit to Harvard Medical School.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceBeijing Jiaotong UniversityBeijingPeople’s Republic of China
  2. 2.Center for Dynamical Biomarkers, Beth Israel Deaconess Medical CenterHarvard Medical SchoolBostonUSA
  3. 3.Key Laboratory of Biomedical Functional MaterialsChina Pharmaceutical UniversityNanjingPeople’s Republic of China
  4. 4.Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical CenterHarvard Medical SchoolBostonUSA
  5. 5.Department of MathematicsSchool of Science, Beijing Jiaotong UniversityBeijingPeople’s Republic of China

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