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Anatomizing the Elo transfer network of Weiqi players

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

Weiqi, also called Go or Baduk, is regarded as the most complicated board game in the world. Weiqi playing has a very long history in East Asia. Its strategic thinking in decision-making even affects militarists there. The availability of the records of almost all Weiqi games in the past decades enables us to perform quantitative studies about this sport with high statistical significance. Here, we construct the directed and undirected Elo transfer networks using over 80,000 Weiqi game records from 1941 to 2019. We investigate the distributions of network measures of the two Elo transfer networks, such as node degree, clustering coefficient, betweenness centrality, and closeness centrality. We find a strong correlation between the average Elo value of a Weiqi player and a few node traits. We also find a rich-club phenomenon among high-Elo players. The two networks are unveiled to possess significant communities, which are consistent with each other and can be well interpreted by player’s affiliation, gender, and Elo value. These findings are different in a large part from those of the chess Elo transfer networks.

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Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The associated data in this manuscript can be access from Go4Go database in the website http://www.go4go.net.]

References

  1. E. Thorp, W.E. Walden, Inf. Sci. 4(1), 1 (1972). https://doi.org/10.1016/0020-0255(72)90002-3

    Article  Google Scholar 

  2. B. Bouzy, T. Cazenave, Artif. Intell. 132(1), 39 (2001). https://doi.org/10.1016/S0004-3702(01)00127-8

    Article  Google Scholar 

  3. B. Georgeot, O. Giraud, EPL 97(6), 68002 (2012). https://doi.org/10.1209/0295-5075/97/68002

    Article  ADS  Google Scholar 

  4. L.G. Xu, M.X. Li, W.X. Zhou, EPL 110(5), 58004 (2015). https://doi.org/10.1209/0295-5075/110/58004

    Article  ADS  Google Scholar 

  5. D. Silver, A. Huang, C.J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, D. Hassabis, Nature 529(7587), 484 (2016). https://doi.org/10.1038/nature16961

    Article  ADS  Google Scholar 

  6. D. Silver, J. Schrittwieser, K. Simonyan, I. Antonoglou, A. Huang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y.T. Chen, T. Lillicrap, H. Fan, L. Sifre, G. van den Driessche, T. Graepel, D. Hassabis, Nature 550(7676), 354 (2017). https://doi.org/10.1038/nature24270

    Article  ADS  Google Scholar 

  7. D. Silver, T. Hubert, J. Schrittwieser, I. Antonoglou, M. Lai, A. Guez, M. Lanctot, L. Sifre, D. Kumaran, T. Graepel, T. Lillicrap, K. Simonyan, D. Hassabis, Science 362(6419), 1140 (2018). https://doi.org/10.1126/science.aar6404

    Article  ADS  MathSciNet  Google Scholar 

  8. G.Y. Zhu, Q.M. Huang, C.S. Xu, L.Y. Xing, W. Gao, H.X. Yao, IEEE Trans. Multimed. 9(6), 1167 (2007). https://doi.org/10.1109/TMM.2007.902847

    Article  Google Scholar 

  9. S. Motegi, N. Masuda, Sci. Rep. 2, 904 (2012). https://doi.org/10.1038/srep00904

    Article  ADS  Google Scholar 

  10. J. Mertz, D.L. Hoover, J.M. Burke, D. Bellar, L.M. Jones, B. Leitzelar, L.W. Judeg, Int. J. Perform. Anal. Sport. 16(3), 737 (2016). https://doi.org/10.1080/24748668.2016.11868925

    Article  Google Scholar 

  11. R. Coulom, in Computers and Games, vol. 5131, ed. by H.J. van den Herik, X.H. Xu, Z.M. Ma, M.H.M. Winands (Springer, Berlin, 2008), pp. 113–124. https://doi.org/10.1007/978-3-540-87608-9_11

  12. R. Gasquez, V. Royuela, Soc. Sci. Q. 97(2), 125 (2016). https://doi.org/10.1111/ssqu.12262

    Article  Google Scholar 

  13. A. Blanch, A. Aluja, M.P. Cornado, Pers. Individ. Differ. 86, 117 (2015). https://doi.org/10.1016/j.paid.2015.06.004

  14. R. Pelanek, Comput. Educ. 98, 169 (2016). https://doi.org/10.1016/j.compedu.2016.03.017

    Article  Google Scholar 

  15. R. Lehmann, K. Wohlrabe, J. Informetr. 11(3), 800 (2017). https://doi.org/10.1016/j.joi.2017.05.004

    Article  Google Scholar 

  16. S. Currarini, M.O. Jackson, P. Pin, Proc. Natl. Acad. Sci. USA 107(11), 4857 (2010). https://doi.org/10.1073/pnas.0911793107

    Article  ADS  Google Scholar 

  17. L. Bargigli, G. di Iasio, L. Infante, F. Lillo, F. Pierobon, Quant. Financ. 15, 673 (2014). https://doi.org/10.1080/14697688.2014.968356

    Article  Google Scholar 

  18. M.X. Li, V. Palchykov, Z.Q. Jiang, K. Kaski, J. Kertész, S. Miccichè, M. Tumminello, W.X. Zhou, R.N. Mantegna, New J. Phys. 16(8), 083038 (2014). https://doi.org/10.1088/1367-2630/16/8/083038

  19. C. Quatman, P. Chelladurai, J. Sport Manag. 22(3), 338 (2008). https://doi.org/10.1123/jsm.22.3.338

    Article  Google Scholar 

  20. M. Pieters, J. Knoben, M. Pouwels, J. Sport Manag. 26(5), 433 (2012). https://doi.org/10.1123/jsm.26.5.433

    Article  Google Scholar 

  21. L. Ferreri, M. Ivaldi, F. Daolio, M. Giacobini, A. Rainoldi, M. Tomassini, Eur. J. Sport Sci. 15(5), 414 (2015). https://doi.org/10.1080/17461391.2014.960007

    Article  Google Scholar 

  22. T.M. Loughead, K. Fransen, S. Van Puyenbroeck, M.D. Hoffmann, B. De Cuyper, N. Vanbeselaere, F. Boen, J. Sports Sci. 34(21), 2063 (2016). https://doi.org/10.1080/02640414.2016.1150601

    Article  Google Scholar 

  23. J. Ribeiro, P. Silva, R. Duarte, K. Davids, J. Garganta, Sports Med. 47(9), 1689 (2017). https://doi.org/10.1007/s40279-017-0695-1

    Article  Google Scholar 

  24. M. Lai, R. Meo, R. Schifanella, E. Sulis, J. Sports Sci. 36(23), 2691 (2018). https://doi.org/10.1080/02640414.2018.1482813

    Article  Google Scholar 

  25. J. Castellano, I. Echeazarra, J. Sports Sci. 37(23), 2631 (2019). https://doi.org/10.1080/02640414.2019.1589919

    Article  Google Scholar 

  26. G.J. Jones, M. Edwards, J.N. Bocarro, K.S. Bunds, J.W. Smith, J. Sport Manag. 31(2), 148 (2017). https://doi.org/10.1123/jsm.2016-0118

    Article  Google Scholar 

  27. M.X. Li, Q.L. Xiao, Y. Wang, W.X. Zhou, Int. J. Mod. Phys. B 32(29), 1850320 (2018). https://doi.org/10.1142/S0217979218503204

    Article  ADS  Google Scholar 

  28. M.X. Li, W.X. Zhou, H.E. Stanley, EPL 125(1), 18005 (2019). https://doi.org/10.1209/0295-5075/125/18005

    Article  ADS  Google Scholar 

  29. N. Almeira, A.L. Schaigorodsky, J.I. Perotti, O.V. Billoni, Sci. Rep. 7, 15186 (2017). https://doi.org/10.1038/s41598-017-15428-z

    Article  ADS  Google Scholar 

  30. M.E.J. Newman, SIAM Rev. 45(2), 167 (2003). https://doi.org/10.1137/S003614450342480

    Article  ADS  MathSciNet  Google Scholar 

  31. R. Albert, A.L. Barabási, Rev. Mod. Phys. 74(1), 47 (2002). https://doi.org/10.1103/RevModPhys.74.47

    Article  ADS  MathSciNet  Google Scholar 

  32. A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51(4), 661 (2009). https://doi.org/10.1137/070710111

    Article  ADS  MathSciNet  Google Scholar 

  33. Z.Q. Jiang, W.J. Xie, M.X. Li, B. Podobnik, W.X. Zhou, H.E. Stanley, Proc. Natl. Acad. Sci. USA 110(5), 1600 (2013). https://doi.org/10.1073/pnas.1220433110

    Article  ADS  Google Scholar 

  34. G. Fagiolo, Phys. Rev. E 76(2), 026107 (2007). https://doi.org/10.1103/PhysRevE.76.026107

    Article  ADS  MathSciNet  Google Scholar 

  35. M.X. Li, Z.Q. Jiang, W.J. Xie, S. Miccichè, M. Tumminello, W.X. Zhou, R.N. Mantegna, Sci. Rep. 4, 5132 (2014). https://doi.org/10.1038/srep05132

    Article  Google Scholar 

  36. S. Zhou, R.J. Mondragón, IEEE Commun. Lett. 8(3), 180 (2004)

  37. Z.Q. Jiang, W.X. Zhou, New J. Phys. 10, 043002 (2008). https://doi.org/10.1088/1367-2630/10/4/043002

    Article  ADS  Google Scholar 

  38. M.E.J. Newman, Proc. Natl. Acad. Sci. USA 103(23), 8577 (2006). https://doi.org/10.1073/pnas.0601602103

  39. M.E.J. Newman, Phys. Rev. E 69, 066133 (2004)

    Article  ADS  Google Scholar 

  40. V.D. Blondel, J.L. Guillaume, R. Lambiotte, E. Lefebvre, J. Stat. Mech. 2008(10), P10008 (2008). https://doi.org/10.1088/1742-5468/2008/10/P10008

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (11605062) and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Research Institute of Sports Economics, East China University of Science and Technology, Shanghai, 200237, China

    Ming-Xia Li

  2. Research Center for Econophysics, East China University of Science and Technology, Shanghai, 200237, China

    Ming-Xia Li & Wei-Xing Zhou

  3. Department of Finance, East China University of Science and Technology, Shanghai, 200237, China

    Ming-Xia Li & Wei-Xing Zhou

  4. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Wei-Xing Zhou

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  1. Ming-Xia Li
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Contributions

Funding acquisition: M-XL and W-XZ; investigation: M-XL; methodology: M-XL and W-XZ; supervision: W-XZ; writing—original draft, M-XL and W-XZ; writing—review and editing: M-XL and W-XZ.

Corresponding author

Correspondence to Wei-Xing Zhou.

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Cite this article

Li, MX., Zhou, WX. Anatomizing the Elo transfer network of Weiqi players. Eur. Phys. J. B 94, 166 (2021). https://doi.org/10.1140/epjb/s10051-021-00180-1

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