Complex network approach to characterize the statistical features of the sunspot series

Yong Zou*, Michael Small, Zonghua Liu, Juergen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)
9 Downloads (Pure)


Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse-transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network that span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15-1000 days by a power-law regime with scaling exponent gamma = 2.04 of the occurrence time of two subsequent strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models.

Original languageEnglish
Article number013051
Number of pages18
JournalNew Journal of Physics
Publication statusPublished - 30 Jan 2014


  • time-series
  • solar-cycle
  • visibility graph
  • grand minima
  • oscillator
  • prediction
  • amplitude
  • phase


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