Mathematical Modeling of Information Diffusion in Social Network
DOI:
https://doi.org/10.52575/2687-0959-2025-57-4-272-278Keywords:
Mathematical Modeling, Social Networks, Information DiffusionAbstract
This work aims to develop a modified diffusion model of information spreading in social networks based on a one-dimensional parabolic equation. The model’s key feature is its strict physical basis for all parameters, enabling a transition from qualitative to quantitative estimates. The study treats information as a continuous function of the number of users distributing the news. The method of integral averaging applied in the model ensures an adequate transition to the discrete structure of the social graph. The novelty of the approach lies in the explicit definition of distributed information sources through the free term of the equation, which includes a Heaviside theta function. This formulation reflects the real activation mechanism of users who become secondary sources. We conducted numerical experiments using real Twitter data on the spread of news about the Higgs boson discovery. The test results demonstrate the model’s high accuracy: the normalized root-mean-square error between the simulated and experimental data was 0,7%. The obtained results confirm the hypothesis about the applicability of physical diffusion laws for describing information flows in social networks.
Acknowledgements
The work was supported by the Azov-Black Sea Mathematical Center (Agreement № 075-02-2025-1608 of February 27, 2025).
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Kempe D, Kleinberg J, Tardos E. Maximizing the Spread of Influence through a Social Network. Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. 2003:137–146.
Daley DJ, Gani J. Epidemic Modelling: An Introduction. Cambridge: Cambridge University Press; 1999. 234 p.
Dritsas E, Trigka M. Machine Learning in Information and Communications Technology: A Survey. Information. 2024;16(1):8. https://doi.org/10.3390/info16010008
Wang F,Wang H, Xu K. Characterizing Information Diffusion in Online Social Networks with Linear DiffusiveModel. 2013 IEEE 33rd International Conference on Distributed Computing Systems. 2013:307–316. https://doi.org/10.1109/ICDCS.2013.14
Hu Y, Song RJ, Chen M. Modeling for Information Diffusion in Online Social Networks via Hydrodynamics. IEEE Access. 2017;5:128–135. https://doi.org/10.1109/ACCESS.2016.2605009
Krivorotko O, Zvonareva T, Zyatkov N. Numerical Solution of the Inverse Problem for Diffusion-Logistic Model Arising in Online Social Networks. In: A. Strekalovsky et al. (eds.) MOTOR 2021, CCIS 1476. Cham: Springer; 2021:444–459. https://doi.org/10.1007/978-3-030-86433-0_31
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