CC BY 3.0 UnportedZou, Y.Small, M.Liu, Z.Kurths, J.2020-08-012020-08-012014https://doi.org/10.34657/3890https://oa.tib.eu/renate/handle/123456789/5261Complex 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 γ = 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.enghttps://creativecommons.org/licenses/by/3.0/530complex networktime-series datasunspotsArticle