Table of Contents Author Guidelines Submit a Manuscript
Complexity
Volume 2018, Article ID 4732491, 11 pages
https://doi.org/10.1155/2018/4732491
Research Article

Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science

School of Business Informatics, National Research University Higher School of Economics, Moscow 101000, Russia

Correspondence should be addressed to Andrey Dmitriev; ur.esh@veirtimd.a

Received 9 August 2018; Accepted 11 November 2018; Published 2 December 2018

Guest Editor: Piotr Brodka

Copyright © 2018 Andrey Dmitriev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. J. De Solla Price, “Networks of scientific papers,” Science, vol. 149, no. 3683, pp. 510–515, 1965. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Barabasi and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. Albert and A. Barabási, “Statistical mechanics of complex networks,” Reviews of Modern Physics, vol. 74, no. 1, pp. 47–97, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. C. T. Butts, “The complexity of social networks: Theoretical and empirical findings,” Social Networks, vol. 23, no. 1, pp. 31–71, 2001. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Skvoretz, “Complexity theory and models for social networks,” Complexity, vol. 8, no. 1, pp. 47–55 (2003), 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. G. Everett, “Role similarity and complexity in social networks,” Social Networks. An International Journal of Structural Analysis, vol. 7, no. 4, pp. 353–359, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  7. H. Ebel, J. Davidsen, and S. Bornholdt, “Dynamics of social networks,” Complexity, vol. 8, no. 2, pp. 24–27 (2003), 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. W. Hwang, “Complex networks: Structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175–308, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Tabassum, F. S. F. Pereira, S. Fernandes, and J. Gama, “Social Networks Analysis: An Overview,” WIREs Data Mining and Knowledge Discovery, pp. 1–21, 2018. View at Google Scholar
  10. S. Saganowski, B. Gliwa, P. Bródka, A. Zygmunt, P. Kazienko, and J. Kozlak, “Predicting community evolution in social networks,” Entropy, vol. 17, no. 5, pp. 3053–3096, 2015. View at Publisher · View at Google Scholar · View at Scopus
  11. P. De Meo, F. Messina, D. Rosaci, and G. M. L. Sarné, “Forming time-stable homogeneous groups into Online Social Networks,” Information Sciences, vol. 414, pp. 117–132, 2017. View at Google Scholar · View at Scopus
  12. A. Grabowski and R. A. Kosiński, “Ising-based model of opinion formation in a complex network of interpersonal interactions,” Physica A: Statistical Mechanics and its Applications, vol. 361, no. 2, pp. 651–664, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Dasgupta, R. K. Pan, and S. Sinha, “Phase of Ising spins on modular networks analogous to social polarization,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 80, no. 2, Article ID 025101, 2009. View at Publisher · View at Google Scholar
  14. G. Bianconi, “Mean Field Solution of the Ising Model on a Barabási-Albert Network,” Physics Letters A, vol. 303, no. 2-3, pp. 166–168, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. Li, F. Liu, and P. Li, “Ising model of user behavior decision in network rumor propagation,” Discrete Dynamics in Nature and Society, vol. 2018, Article ID 5207475, 2018. View at Publisher · View at Google Scholar · View at MathSciNet
  16. J.-L. Guo, Q. Suo, A.-Z. Shen, and J. Forrest, “The evolution of hyperedge cardinalities and bose-Einstein condensation in hypernetworks,” Scientific Reports, vol. 6, Article ID 33651, 2016. View at Google Scholar · View at Scopus
  17. M. Faccin, T. Johnson, J. Biamonte, S. Kais, and P. Migdał, “Degree Distribution in Quantum Walks on Complex Networks,” Physical Review X, vol. 3, no. 4, Article ID 041007, 2013. View at Publisher · View at Google Scholar
  18. J. Reichardt and S. Bornholdt, “Statistical mechanics of community detection,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 74, no. 1, Article ID 016110, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. B. P. Chamberlain, J. Levy-Kramer, C. Humby, and M. P. Deisenroth, “Real-time community detection in full social networks on a laptop,” PLoS ONE, vol. 13, no. 1, Article ID e0188702, 2018. View at Google Scholar · View at Scopus
  20. Y. Matsubara, Y. Sakurai, B. A. Prakash, L. Li, and C. Faloutsos, “Nonlinear dynamics of information diffusion in social networks,” ACM Transactions on the Web (TWEB), vol. 11, Article 11, no. 2, 2017. View at Google Scholar · View at Scopus
  21. N. Hegde, L. Massoulie, and L. Viennot, “Self-organizing flows in social networks,” Theoretical Computer Science, vol. 584, no. 13, pp. 3–18, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  22. P. Bak, C. Tang, and K. Wiesenfeld, “Self-organized Criticality: An Explanation of 1/f-noise,” Physical Review Letters, vol. 59, no. 4, pp. 381–384, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  23. P. Bak, C. Tang, and K. Wiesenfeld, “Self-organized Criticality,” Physical Review A, vol. 38, no. 1, pp. 364–374, 1988. View at Google Scholar
  24. P. Bak, How Nature Works: The Science of Self-organized Criticality, Springer-Verlag, 1996. View at MathSciNet
  25. B. Tadić, M. M. Dankulov, and R. Melnik, “Mechanisms of self-organized criticality in social processes of knowledge creation,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 96, no. 3, Article ID 032307, 2017. View at Publisher · View at Google Scholar
  26. M. Aguilera, I. Morer, X. Barandiaran, and M. Bedia, “Quantifying Political Self-Organization in Social Media. Fractal patterns in the Spanish 15M movement on Twitter,” in Proceedings of the 12th European Conference on Artificial Life, pp. 395–402, Michigan, USA, 2013. View at Publisher · View at Google Scholar
  27. K. Lyudmyla, B. Vitalii, and R. Tamara, “Fractal time series analysis of social network activities,” in Proceedings of the 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T), pp. 456–459, IEEE, Kharkov, Ukraine, October 2017. View at Publisher · View at Google Scholar
  28. T. De Bie, J. Lijffijt, C. Mesnage, and R. Santos-Rodriguez, “Detecting trends in twitter time series,” in Proceedings of the 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6, Vietri sul Mare, Salerno, Italy, September 2016. View at Publisher · View at Google Scholar
  29. A. Mollgaard and J. Mathiesen, “Emergent user behavior on twitter modelled by a stochastic differential equation,” PLoS ONE, vol. 10, no. 5, pp. 1–12, 2015. View at Google Scholar · View at Scopus
  30. A. Dmitriev, V. Dmitriev, O. Tsukanova, and S. Maltseva, “A nonlinear dynamical approach to the interpretation of microblogging network complexity,” Studies in Computational Intelligence, vol. 689, pp. 390–400, 2017. View at Google Scholar · View at Scopus
  31. B. Tadić, V. Gligorijević, M. Mitrović, and M. Šuvakov, “Co-evolutionary mechanisms of emotional bursts in online social dynamics and networks,” Entropy, vol. 15, no. 12, pp. 5084–5120, 2013. View at Publisher · View at Google Scholar · View at Scopus
  32. М. М. Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos, Touchstone, New York, USA, 1993.
  33. O. A. Tsukanova, E. P. Vishnyakova, and S. V. Maltseva, “Model-based monitoring and analysis of the network community dynamics in a textured state space,” in Proceedings of the 16th IEEE Conference on Business Informatics, CBI 2014, pp. 44–49, Switzerland, July 2014. View at Scopus
  34. Ming Li, “Fractal Time Series—A Tutorial Review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  35. P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D: Nonlinear Phenomena, vol. 9, no. 1-2, pp. 189–208, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. M. Z. Ding, C. Grebogi, E. Ott, T. Sauer, and J. A. Yorke, “Estimating correlation dimension from a chaotic time series: when does plateau onset occur?” Physica D: Nonlinear Phenomena, vol. 69, no. 3-4, pp. 404–424, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  37. M. M. Dubovikov, N. V. Starchenko, and M. S. Dubovikov, “Dimension of the minimal cover and fractal analysis of time series,” Physica A: Statistical Mechanics and its Applications, vol. 339, no. 3-4, pp. 591–608, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. B. B. Mandelbrot and J. W. Van Ness, “Fractional brownian motions, fractional noises and applications,” SIAM, vol. 10, no. 4, pp. 422–437, 1968. View at Publisher · View at Google Scholar · View at MathSciNet
  39. R. B. D’Agostino, A. Belanger, and R. B. D’Agostino, “A suggestion for using powerful and informative tests of normality,” The American Statistician, vol. 44, no. 4, pp. 316–321, 1990. View at Google Scholar · View at Scopus
  40. R. B. Govindan, J. D. Wilson, H. Preil, H. Eswaran, J. Q. Campbell, and C. L. Lowery, “Detrended fluctuation analysis of short datasets: an application to fetal cardiac data,” Physica D: Nonlinear Phenomena, vol. 226, no. 1, pp. 23–31, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  41. M. M. Uddin, M. Imran, and H. Sajjad, “Understanding Types of Users on Twitter,” in Proceedings of 6th ASE International Conference in Social Computing, Stanford, USA, 2014.
  42. A. I. Olemskoi, A. V. Khomenko, and D. O. Kharchenko, “Self-organized criticality within fractional Lorenz scheme,” Physica A: Statistical Mechanics and its Applications, vol. 323, no. 1-4, pp. 263–293, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  43. A. I. Olemskoǐ, “Theory of stochastic systems with singular multiplicative noise,” Physics-Uspekhi, vol. 41, no. 3, pp. 269–301, 1998. View at Publisher · View at Google Scholar · View at Scopus
  44. A. I. Olemskoi and A. V. Khomenko, “Three-Parameter Kinetics of a Phase Transition,” Journal of Theoretical and Experimental Physics, vol. 81, no. 6, pp. 1180–1192, 1996. View at Google Scholar
  45. S. Aparicio, J. Villazón-Terrazas, and G. Álvarez, “A Model for Scale-Free Networks: Application to Twitter,” Entropy, vol. 17, no. 12, pp. 5848–5867, 2015. View at Publisher · View at Google Scholar