In recent years, with the spread of social networking services (SNSs), communication has been facilitated among people regardless of age, occupation, and geographical locations. The SNSs are used not only for directly developing friendships, but also as a tool for spreading friendships, allowing users to exchange information in real-time with people having common interests. Twitter, in particular, is a service with a large number of users and a considerable influence on information diffusion. In this study, the characteristics of the follower networks centered on various Twitter influencers are analyzed, and the common characteristics that do not depend on individual influencers are clarified for the world-famous influencers (US and international). Furthermore, after theoretically analyzing the relationship between the characteristics of the nodal degree distribution and the degree correlation, the degree dependence of the correlation coefficient expressing the degree correlation is clarified using numerical experiments.

1. [1] L. C. Freeman, “Centrality in social networks conceptual clarification,” Social Networks, Vol.1, No.3, pp. 215-239, 1978.
2. [2] L. C. Freeman, S. P. Borgatti, and D. R. White, “Centrality in valued graphs: A measure of betweenness based on network flow,” Social Networks, Vol.13, No.2, pp. 141-154, 1991.
3. [3] P. J. Carrington, J. Scott, and S. Wasserman (Eds.), “Models and methods in social network analysis,” Cambridge University Press, 2005.
4. [4] K. Stephenson and M. Zelen, “Rethinking centrality: Methods and examples,” Social Networks, Vol.11, No.1, pp. 1-37, 1989.
5. [5] M. A. Al-Garadi, K. D. Varathan, S. D. Ravana et al., “Analysis of Online Social Network Connections for Identification of Influential Users: Survey and Open Research Issues,” ACM Computing Surveys, Vol.51, Issue 1, Article No.16, pp. 1-37, 2019.
6. [6] Y. Wang, G. Cong, G. Song, and K. Xie, “Community-based greedy algorithm for mining top-K influential nodes in mobile social networks,” Proc. of the 16th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, pp. 1039-1048, 2010.
7. [7] W. Chen, Y. Wang, and S. Yang, “Efficient influence maximization in social networks,” Proc. of the 15th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, pp. 199-208, 2009.
8. [8] H. Li, J.-T. Cui, and J.-F. Ma, “Social influence study in online networks: A three-level review,” J. of Computer Science and Technology, Vol.30, pp. 184-199, 2015.
9. [9] E. S. Kim and S. S. Han, “An analytical way to find influencers on social networks and validate their effects in disseminating social games,” IEEE Int. Conf. on Advances in Social Network Analysis and Mining (ASONAM’09), pp. 41-46, 2009.
10. [10] M. Cha, H. Haddadi, F. Benevenuto, and K. P. Gummadi, “Measuring user influence in Twitter: The million follower fallacy,” Proc. of 4th Int. AAAI Conf. on Weblogs and Social Media (ICWSM), Vol.4, No.1, 2010.
11. [11] D. M. Romero, W. Galuba, S. Asur, and B. A. Huberman, “Influence and Passivity in Social Media,” Proc. of the 20th Int. Conf. Companion on World Wide Web, pp. 113-114, 2011.
12. [12] M. Kitsak, L. K. Gallos, S. Havlin, F. Liljeros, L. Muchnik, H. E. Stanley, and H. A. Makse, “Identification of influential spreaders in complex networks,” Nature Physics, Vol.6, pp. 888-893, 2010.
13. [13] A. Sheikhahmadi and M. A. Nematbakhsh, “Identification of multi-spreader users in social networks for viral marketing,” J. of Information Science, Vol.43, Issue 3, pp. 412-423, 2017.
14. [14] Y. Mei, Y. Zhong, and J. Yang, “Finding and analyzing principal features for measuring user influence on Twitter,” Proc. of IEEE 1st Int. Conf. on Big Data Computing Service and Applications (BigDataService’15), pp. 478-486, 2015.
15. [15] Q. Sun, N. Wang, Y. Zhou, and Z. Luo, “Identification of influential online social network users based on multi-features,” Int. J. of Pattern Recognition and Artificial Intelligence, Vol.30, No.6, Article No.1659015, 2016.
16. [16] C. Takano and M. Aida, “Proposal of new index for describing node centralities based on oscillation dynamics on network,” IEEE Global Communications Conf. (GLOBECOM), 2016.
17. [17] C. Takano and M. Aida, “Fundamental framework for describing various node centralities using an oscillation model on social media networks,” IEEE Int. Conf. on Communications (ICC), 2017.
18. [18] C. Takano and M. Aida, “Decay characteristics of user dynamics in online social networks,” IEEE Access, Vol.8, pp. 73986-73991, 2020.
19. [19] A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, Vol.286, Issue 5439, pp. 509-512, 1999.
20. [20] L. A. Adamic and B. A. Huberman, “Power-law distribution of the world wide web,” Science, Vol.287, Issue 5461, p. 2115, 2000.
21. [21] M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Random graphs with arbitrary degree distributions and their applications,” Phys. Rev. E, Vol.64, Issue 2, Article No.026118, 2001.
22. [22] D. J. Watts and S. H. Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature, Vol.393, pp. 440-442, 1998.
23. [23] F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y. Åberg, “The web of human sexual contacts,” Nature, Vol.411, pp. 907-908, 2001.
24. [24] W. Willinger, D. L. Alderson, and J. C. Doyle, “Mathematics and the Internet: A Source of Enormous Confusion and Great Potential,” Notices of the American Mathematical Society, Vol.56, No.5, pp. 586-599, 2009.
25. [25] M. E. J. Newman, “Assortative mixing in networks,” Phys. Rev. Lett., Vol.89, Issue 20, Article No.208701, 2002.
26. [26] B. Fotouhi and M. G. Rabbat, “Degree Correlation in Scale-Free Graphs,” The European Physical J. B, Vol.86, No.510, 2013.
27. [27] A.-L. Barabáshi, “Network Science,” Cambridge University Press, 2016.
28. [28] O. Williams and C. I. D. Genio, “Degree correlations in directed scale-free networks,” PLOS ONE, Vol.9, No.10, Article No.e110121, 2014.
29. [29] H. Kim, C. I. D. Genio, K. E. Bassler, and Z. Toroczkai, “Constructing and sampling directed graphs with given degree sequences,” New J. of Physics, Vol.14, Article No.023012, 2012.
30. [30] H. Kwak, C. Lee, H. Park, and S. Moon, “What is Twitter, a social network or a news media?,” Proc. of the 19th Int. Conf. on World Wide Web (WWW ’10), pp. 591-600, 2010.
31. [31] S. A. Myers, A. Sharma, P. Gupta, and J. Lin, “Information network or social network?: the structure of the twitter follow graph,” Proc. of the 23rd Int. Conf. on World Wide Web (WWW ’14), pp. 493-498, 2014.
32. [32] R. Albert, H. Jeong, and A.-L. Barabási, “Diameter of the world-wide web,” Nature, Vol.401, pp. 130-131, 1999.
33. [33] M. Faloutsos, P. Faloutsos, and C. Faloutsos, “On power-law relationships of the internet topology,” ACM SIGCOMM Computer Communication Review, Vol.29, Issue 4, pp. 251-262, 1999.
34. [34] A.-L. Barabási and Z. N. Oltvai, “Network biology: understanding the cell’s functional organization,” Nature Reviews Genetics, Vol.5, pp. 101-113, 2004.
35. [35] A.-L. Barabási, “Network Science Degree Correlation,” http://barabasi.com/f/620.pdf [accessed March 31, 2021]
36. [36] J. Mathiesen, P. Yde, and M. H. Jensen, “Modular networks of word correlations on Twitter,” Scientific Reports, Vol.2, Article No.814, 2012.