Abstract
Online social networks suffer from explosive user dynamics such as flaming that can seriously affect social activities in the real world because the dynamics have growth rates that can overwhelm our rational decision making faculties. Therefore, a deeper understanding of user dynamics in online social networks is a fundamental problem in computer and information science. One of the effective user dynamics models is the networked oscillation model; it uses a second-order differential equation with Laplacian matrix. Although our previous study indicates that the oscillation model provides us with a minimal but effective model of user interactions, there still remains the open problem as to the existence of a first-order fundamental differential equation that respects the structure of the original network. This paper fills in this gap and shows that, by doubling the dimension of the state space, we can explicitly but naturally construct a fundamental equation that fully respects the structure of the original network.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Nekovee, M., Moreno, Y., Bianconi, G., Marsili, M.: Theory of rumour spreading in complex social networks. Phys. A Stat. Mech. Appl. 374(1), 457–470 (2007)
Cannarella, J., Spechler, J.A.: Epidemiological modeling of online social network dynamics (2014). arXiv: 1401.4208
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)
Wang, L., Xiao, F.: Finite-time consensus problems for networks of dynamic agents. IEEE Trans. Autom. Control 55(4), 950–955 (2010)
Snijders, T.A.B., Koskinen, J., Schweinberger, M.: Maximum likelihood estimation for social network dynamics. IEEE Trans. Autom. Control 4(2), 567–588 (2010)
Cha, M., Mislove, A., Gummadi, K.P.: A measurement-driven analysis of information propagation in the Flickr social network. In: Proceedings of the 18th International Conference on World Wide Web (WWW’09), pp. 721–730 (2009)
Zhao, X., Sala, A., Wilson, C., Wang, X., Gaito, S., Zheng, H., Zhao, B.Y.: Multi-scale dynamics in a massive online social network. In: Proceedings of the 2012 Internet Measurement Conference (IMC’12), pp. 171–184 (2012)
Aida, M., Takano, C., Murata, M.: Oscillation model for describing network dynamics caused by asymmetric node interaction. IEICE Trans. Commun. E101-B(1), 123–136 (2018)
Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)
Carrington, P.J., Scott, J., Wasserman, S.: Models and Methods in Social Network Analysis. Cambridge University Press, Cambridge (2005)
Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the ACM SIGCOMM Conference on Internet Measurement, pp. 29–42 (2007)
Takano, C., Aida, M.: Revealing of the underlying mechanism of different node centralities based on oscillation dynamics on networks. IEICE Trans. Commun. E101-B(8), 1820–1832 (2018)
Brewer, J.: Kronecker products and matrix calculus in system theory. IEEE Trans. Circuits Syst. 25(9), 772–781 (1978)
Bjorken, J.D., Drell, S.D.: Relativistic Quantum Mechanics. McGraw-Hill, New York (1965)
Aida, M.: Introduction to Network Dynamics. Morikita Publishing, Tokyo (2020)
Acknowledgements
This research was supported by Grant-in-Aid for Scientific Research (B) No. 17H01737 (2017–2019) and No. 19H04096 (2019–2021), and Grant-in-Aid for Scientific Research (C) No. 18K11271 (2018–2020) and No. 18K13777 (2018–2020) from the Japan Society for the Promotion of Science (JSPS).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Aida, M., Takano, C., Ogura, M. (2020). On the Fundamental Equation of User Dynamics and the Structure of Online Social Networks. In: Masuda, N., Goh, KI., Jia, T., Yamanoi, J., Sayama, H. (eds) Proceedings of NetSci-X 2020: Sixth International Winter School and Conference on Network Science. NetSci-X 2020. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-38965-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-38965-9_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38964-2
Online ISBN: 978-3-030-38965-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)