{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:33:30Z","timestamp":1760236410124,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T00:00:00Z","timestamp":1637539200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971421"],"award-info":[{"award-number":["11971421"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Solar magnetic activity exhibits a complex nonlinear behavior, but its dynamic process has not been fully understood. As the complex network technique can better capture the dynamics of nonlinear system, the visibility graphs (VG), the horizontal visibility graphs (HVG), and the limited penetrable visibility graphs (LPVG) are applied to implement the mapping of sunspot relative numbers in the northern and southern hemispheres. The results show that these three methods can capture important information of nonlinear dynamics existing in the long-term hemispheric sunspot activity. In the presentation of the results, the network degree sequence of the HVG method changes preferentially to the original data series as well as the VG and the LPVG, while both the VG and the LPVG slightly lag behind the original time series, which provides some new ideas for the nonlinear dynamics of the hemispheric asymmetry in the two hemispheres. Meanwhile, the use of statistical feature-skewness values and complex network visibility graphs can yield some complementary information for mutual verification.<\/jats:p>","DOI":"10.3390\/sym13112228","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T03:12:40Z","timestamp":1638328360000},"page":"2228","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The North\u2013South Asymmetry of Sunspot Relative Numbers Based on Complex Network Technique"],"prefix":"10.3390","volume":"13","author":[{"given":"Hengyu","family":"Xu","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China"}]},{"given":"Yu","family":"Fei","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China"}]},{"given":"Chun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China"}]},{"given":"Jiajuan","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Statistics, BNU-HKBU United International College, 2000 Jintong Road, TangJiaWan, Zhuhai 519087, China"}]},{"given":"Xinan","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing 402160, China"}]},{"given":"Zhongjie","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing 402160, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,22]]},"reference":[{"key":"ref_1","first-page":"251","article-title":"Prof. Spoerer\u2019s researches on Sun-spots","volume":"50","author":"Spoerer","year":"1890","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1093\/mnras\/64.8.747","article-title":"Note on the distribution of sun-spots in heliographic latitude, 1874\u20131902","volume":"64","author":"Maunder","year":"1904","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Newton, H.W., and Milsom, A.S. (1955). Note on the observed differences in spottedness of the Sun\u2019s northern and southern hemispheres. Mon. Not. R. Astron. Soc., 398\u2013404.","DOI":"10.1093\/mnras\/115.4.398"},{"key":"ref_4","first-page":"283","article-title":"Solar coronal mass ejections and flares","volume":"162","author":"Harrison","year":"1986","journal-title":"Astron. Astrophys."},{"key":"ref_5","first-page":"201","article-title":"North-south asymmetry in the solar flare index","volume":"166","year":"1996","journal-title":"Sol. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"A34","DOI":"10.1051\/swsc\/2017038","article-title":"Statistical properties of solar H\u03b1 flare activity","volume":"7","author":"Deng","year":"2017","journal-title":"J. Space Weather Space Clim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1093\/mnras\/stz1653","article-title":"Phase and amplitude asymmetry in the quasi-biennial oscillation of solar H\u03b1 flare activity","volume":"488","author":"Deng","year":"2019","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5442","DOI":"10.1093\/mnras\/staa2863","article-title":"Evidence of a strong relationship between hemispheric asymmetry in solar coronal rotation and solar activity during solar cycle 24","volume":"499","author":"Sharma","year":"2020","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4952","DOI":"10.1093\/mnras\/stab1959","article-title":"Differential rotation of the solar transition region from STEREO\/EUVI 30.4-nm images","volume":"506","author":"Sharma","year":"2021","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s12036-012-9143-7","article-title":"The hemispheric asymmetry of polar faculae","volume":"33","author":"Deng","year":"2012","journal-title":"J. Astrophys. Astron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.asr.2012.08.013","article-title":"The hemispheric asynchrony of polar faculae during solar cycles 19\u201322","volume":"51","author":"Deng","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_12","first-page":"265","article-title":"Observations tending to investigate the nature of the sun, in order to find the causes or symptoms of its variable emission of light and heat; with remarks on the use that may possibly be drawn from solar observations","volume":"91","author":"Herschel","year":"1801","journal-title":"Philos. Trans. R. Soc. Lond."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Eddy, J.A. (1976). The maunder minimum. Science, 1189\u20131202.","DOI":"10.1126\/science.192.4245.1189"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1029\/JC084iC02p00753","article-title":"Distribution of solar cycle signal in surface air temperature over North America","volume":"84","author":"Currie","year":"1979","journal-title":"J. Geophys. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1126\/science.254.5032.698","article-title":"Length of the solar cycle: An indicator of solar activity closely associated with climate","volume":"254","author":"Lassen","year":"1991","journal-title":"Science"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1126\/science.272.5264.981","article-title":"The impact of solar variability on climate","volume":"272","author":"Haigh","year":"1996","journal-title":"Science"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1.18","DOI":"10.1111\/j.1468-4004.2007.48118.x","article-title":"Cosmoclimatology: A new theory emerges","volume":"48","author":"Svensmark","year":"2007","journal-title":"Astron. Geophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/BF00153057","article-title":"Some comments on the east-west solar flare distribution during the 1976\u20131985 period","volume":"126","author":"Heras","year":"1990","journal-title":"Sol. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.asr.2014.03.006","article-title":"On mid-term periodicities of high-latitude solar activity","volume":"54","author":"Deng","year":"2014","journal-title":"Adv. Space Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"70","DOI":"10.3847\/0004-6256\/151\/3\/70","article-title":"Systematic regularity of hemispheric sunspot areas over the past 140 years","volume":"151","author":"Deng","year":"2016","journal-title":"Astron. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1134\/S0016793218070125","article-title":"Latitude-longitude characteristics of the north-south asymmetry of solar activity","volume":"58","author":"Kramynin","year":"2018","journal-title":"Geomagn. Aeron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1088\/1674-4527\/13\/1\/011","article-title":"Phase analysis of sunspot group numbers on both solar hemispheres","volume":"13","author":"Deng","year":"2013","journal-title":"Res. Astron. Astrophys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1051\/0004-6361:20011068","article-title":"Solar cycle forecasting: A nonlinear dynamics approach","volume":"377","author":"Sello","year":"2001","journal-title":"Astron. Astrophys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"35622","DOI":"10.1038\/srep35622","article-title":"Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series","volume":"6","author":"Gao","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4972","DOI":"10.1073\/pnas.0709247105","article-title":"From time series to complex networks: The visibility graph","volume":"105","author":"Lucas","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_26","first-page":"046103","article-title":"Horizontal visibility graphs: Exact results for random time series","volume":"80","author":"Luque","year":"2009","journal-title":"Phys. Rev."},{"key":"ref_27","first-page":"3","article-title":"Limited penetrable visibility graph for establishing complex network from time series","volume":"61","author":"Zhou","year":"2012","journal-title":"Acta Phys. Sin."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"657","DOI":"10.5194\/npg-19-657-2012","article-title":"Multifractal analysis of solar flare indices and their horizontal visibility graphs","volume":"19","author":"Yu","year":"2012","journal-title":"Nonlinear Process. Geophys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s11207-013-0332-6","article-title":"Visibility-graph analysis of the solar wind velocity","volume":"289","author":"Suyal","year":"2014","journal-title":"Sol. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.5194\/npg-21-1113-2014","article-title":"Long-term changes in the north-south asymmetry of solar activity: A nonlinear dynamics characterization using visibility graphs","volume":"21","author":"Zou","year":"2014","journal-title":"Nonlinear Process. Geophys."},{"key":"ref_31","first-page":"483","article-title":"Long-term monitoring studies of the Sun at the National Astronomical Observatory of Japan","volume":"140","author":"Sakurai","year":"1998","journal-title":"ASP Conf. Ser."},{"key":"ref_32","first-page":"71","article-title":"Sunspot relative numbers observed before 1948 at the Tokyo Astronomical Observatory","volume":"1","author":"Natori","year":"1991","journal-title":"Rep. Natl. Astron. Obs. Jpn."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s11214-014-0074-2","article-title":"Revisiting the Sunspot Number. A 400-Year Perspective on the Solar Cycle","volume":"186","author":"Clette","year":"2014","journal-title":"Space Sci. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1093\/mnras\/stz3136","article-title":"Systematic regularity of solar coronal rotation during the time interval 1939\u20132019","volume":"491","author":"Deng","year":"2020","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_35","first-page":"497","article-title":"On the asymmetry of solar activity","volume":"274","author":"Carbonell","year":"1993","journal-title":"Astron. Astrophys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1002\/asna.201011410","article-title":"Secular variation of hemispheric phase differences in the solar cycle","volume":"331","author":"Zolotova","year":"2010","journal-title":"Astron. Nachrichten."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/2228\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:33:47Z","timestamp":1760168027000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/2228"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,22]]},"references-count":36,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["sym13112228"],"URL":"https:\/\/doi.org\/10.3390\/sym13112228","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,11,22]]}}}