Realistic modelling of information spread using peer-to-peer diffusion patterns

Abstract

In computational social science, epidemic-inspired spread models have been widely used to simulate information diffusion. However, recent empirical studies suggest that simple epidemic-like models typically fail to generate the structure of real-world diffusion trees. Such discrepancy calls for a better understanding of how information spreads from person to person in real-world social networks. Here, we analyse comprehensive diffusion records and associated social networks in three distinct online social platforms. We find that the diffusion probability along a social tie follows a power-law relationship with the numbers of disseminator’s followers and receiver’s followees. To develop a more realistic model of information diffusion, we incorporate this finding together with a heterogeneous response time into a cascade model. After adjusting for observational bias, the proposed model reproduces key structural features of real-world diffusion trees across the three platforms. Our finding provides a practical approach to designing more realistic generative models of information diffusion.

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Fig. 1: The unadjusted diffusion probability \({\it{\Lambda }}_{{\it{k}}_{\it{d}},{\it{k}}_{\it{r}}}\) following (kd,kr) links.
Fig. 2: The power-law relationship between peer-to-peer diffusion probability and users’ degrees.
Fig. 3: The power-law distributions of response time τ.
Fig. 4: Comparison of distributions of diffusion tree size N, depth L and structural virality D.
Fig. 5: Distributions of the lifetime T of diffusion trees.
Fig. 6: A consistency check for the observational bias correction using LiveJournal data.

Data availability

Weibo and Twitter data are publicly available at https://www.dcjingsai.com/v2/cmptDetail.html?id=166 (in Mandarin) and https://snap.stanford.edu/data/higgs-twitter.html. LiveJournal data are subject to restrictions for user privacy protection. Interested readers should contact L. Muchnik (lev.muchnik@huji.ac.il) to gain access to the LiveJournal dataset.

Code availability

Custom code that supports the findings of this study is available at https://github.com/bnzu/main-code-of-rmis.

References

  1. 1.

    Watts, D. J. & Dodds, P. S. Influentials, networks, and public opinion formation. J. Consum. Res. 34, 441–458 (2007).

    Google Scholar 

  2. 2.

    Rogers, E. M. Diffusion of Innovations (Simon and Schuster, 2010).

  3. 3.

    Leskovec, J., Adamic, L. A. & Huberman, B. A. The dynamics of viral marketing. ACM Trans. Web 1, 5 (2007).

    Google Scholar 

  4. 4.

    Centola, D. The spread of behavior in an online social network experiment. Science 329, 1194–1197 (2010).

    CAS  Google Scholar 

  5. 5.

    Aral, S. & Walker, D. Creating social contagion through viral product design: a randomized trial of peer influence in networks. Manag. Sci. 57, 1623–1639 (2011).

    Google Scholar 

  6. 6.

    Newman, M., Barabási, A. L. & Watts, D. J. The Structure and Dynamics of Networks (Princeton Univ. Press, 2011).

  7. 7.

    Vosoughi, S., Roy, D. & Aral, S. The spread of true and false news online. Science 359, 1146–1151 (2018).

    CAS  Google Scholar 

  8. 8.

    Iribarren, J. L. & Moro, E. Impact of human activity patterns on the dynamics of information diffusion. Phys. Rev. Lett. 103, 038702 (2009).

    Google Scholar 

  9. 9.

    Salganik, M. J., Dodds, P. S. & Watts, D. J. Experimental study of inequality and unpredictability in an artificial cultural market. Science 311, 854–856 (2006).

    CAS  Google Scholar 

  10. 10.

    Aral, S., Muchnik, L. & Sundararajan, A. Engineering social contagions: optimal network seeding in the presence of homophily. Netw. Sci. 1, 125–153 (2013).

    Google Scholar 

  11. 11.

    Aral, S. & Walker, D. Identifying influential and susceptible members of social networks. Science 337, 337–341 (2012).

    CAS  Google Scholar 

  12. 12.

    Kwak, H., Lee, C., Park, H. & Moon, S. What is Twitter, a social network or a news media? In Proc. 19th International Conference on World Wide Web 591–600 (ACM, 2010).

  13. 13.

    Gruhl, D., Guha, R., Liben-Nowell, D. & Tomkins, A. Information diffusion through blogspace. In Proc. 13th International Conference on World Wide Web 491–501 (ACM, 2004).

  14. 14.

    Liben-Nowell, D. & Kleinberg, J. Tracing information flow on a global scale using Internet chain-letter data. Proc. Natl Acad. Sci. USA 105, 4633–4638 (2008).

    CAS  Google Scholar 

  15. 15.

    Goel, S., Anderson, A., Hofman, J. & Watts, D. J. The structural virality of online diffusion. Manag. Sci. 62, 180–196 (2015).

    Google Scholar 

  16. 16.

    Goel, S., Watts, D. J. & Goldstein, D. G. The structure of online diffusion networks. In Proc. 13th ACM Conference on Electronic Commerce 623–638 (ACM, 2012).

  17. 17.

    Pei, S., Muchnik, L., Tang, S., Zheng, Z. & Makse, H. A. Exploring the complex pattern of information spreading in online blog communities. PLoS ONE 10, e0126894 (2015).

    Google Scholar 

  18. 18.

    Muchnik, L., Aral, S. & Taylor, S. J. Social influence bias: a randomized experiment. Science 341, 647–651 (2013).

    CAS  Google Scholar 

  19. 19.

    Bapna, R., Ramaprasad, J., Shmueli, G. & Umyarov, A. One-way mirrors in online dating: a randomized field experiment. Manag. Sci. 62, 3100–3122 (2016).

    Google Scholar 

  20. 20.

    Eckles, D., Kizilcec, R. F. & Bakshy, E. Estimating peer effects in networks with peer encouragement designs. Proc. Natl Acad. Sci. USA 113, 7316–7322 (2016).

    CAS  Google Scholar 

  21. 21.

    Centola, D. An experimental study of homophily in the adoption of health behavior. Science 334, 1269–1272 (2011).

    CAS  Google Scholar 

  22. 22.

    Goldenberg, J., Libai, B. & Muller, E. Talk of the network: a complex systems look at the underlying process of word-of-mouth. Mark. Lett. 12, 211–223 (2001).

    Google Scholar 

  23. 23.

    Watts, D. J. A simple model of global cascades on random networks. Proc. Natl Acad. Sci. USA 99, 5766–5771 (2002).

    CAS  Google Scholar 

  24. 24.

    Castellano, C., Fortunato, S. & Loreto, V. Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591 (2009).

    Google Scholar 

  25. 25.

    Zhang, Z. K. et al. Dynamics of information diffusion and its applications on complex networks. Phys. Rep. 651, 1–34 (2016).

    Google Scholar 

  26. 26.

    Pei, S. & Makse, H. A. Spreading dynamics in complex networks. J. Stat. Mech. 2013, P12002 (2013).

    Google Scholar 

  27. 27.

    Domingos, P. & Richardson, M. Mining the network value of customers. In Proc. 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 57–66 (ACM, 2001).

  28. 28.

    Kempe, D., Kleinberg, J. & Tardos, É. Maximizing the spread of influence through a social network. In Proc. 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 137–146 (ACM, 2003).

  29. 29.

    Kitsak, M. et al. Identification of influential spreaders in complex networks. Nat. Phys. 6, 888–893 (2010).

    CAS  Google Scholar 

  30. 30.

    Lü, L. et al. Vital nodes identification in complex networks. Phys. Rep. 650, 1–63 (2016).

    Google Scholar 

  31. 31.

    Hu, Y. et al. Local structure can identify and quantify influential global spreaders in large scale social networks. Proc. Natl Acad. Sci. USA 115, 7468–7472 (2018).

    CAS  Google Scholar 

  32. 32.

    Aral, S. & Dhillon, P. S. Social influence maximization under empirical influence models. Nat. Hum. Behav. 2, 375 (2018).

    Google Scholar 

  33. 33.

    Pei, S., Wang, J., Morone, F. & Makse, H. A. Influencer identification in dynamical complex systems. J. Complex Netw. 8, cnz029 (2020).

  34. 34.

    Moreno, Y., Nekovee, M. & Pacheco, A. F. Dynamics of rumor spreading in complex networks. Phys. Rev. E 69, 066130 (2004).

    Google Scholar 

  35. 35.

    Kermack, W. O. & McKendrick, A. G. A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A. 115, 700–721 (1927).

    Google Scholar 

  36. 36.

    Pastor-Satorras, R., Castellano, C., Van Mieghem, P. & Vespignani, A. Epidemic processes in complex networks. Rev. Mod. Phys. 87, 925 (2015).

    Google Scholar 

  37. 37.

    Iribarren, J. L. & Moro, E. Branching dynamics of viral information spreading. Phys. Rev. E 84, 046116 (2011).

    Google Scholar 

  38. 38.

    Centola, D. & Macy, M. Complex contagions and the weakness of long ties. Am. J. Sociol. 113, 702–734 (2007).

    Google Scholar 

  39. 39.

    De Domenico, M., Lima, A., Mougel, P. & Musolesi, M. The anatomy of a scientific rumor. Sci. Rep. 3, 2980 (2013).

    Google Scholar 

  40. 40.

    Stephen, A. T., Dover, Y., Muchnik, L. & Goldenberg, J. Pump it out! The effect of transmitter activity on content propagation in social media. Saïd Business School WP https://doi.org/10.2139/ssrn.2897582 (2017).

  41. 41.

    Rodriguez, M. G., Gummadi, K. & Schoelkopf, B. Quantifying information overload in social media and its impact on social contagions. In Proc. 8th International AAAI Conference on Weblogs and Social Media 170–179 (AAAI, 2014).

  42. 42.

    Weng, L., Flammini, A., Vespignani, A. & Menczer, F. Competition among memes in a world with limited attention. Sci. Rep. 2, 335 (2012).

    CAS  Google Scholar 

  43. 43.

    Gleeson, J. P., Ward, J. A., O’Sullivan, K. P. & Lee, W. T. Competition-induced criticality in a model of meme popularity. Phys. Rev. Lett. 112, 048701 (2014).

    Google Scholar 

  44. 44.

    Feng, L. et al. Competing for attention in social media under information overload conditions. PLoS ONE 10, e0126090 (2015).

    Google Scholar 

  45. 45.

    Hodas, N. O. & Lerman, K. How visibility and divided attention constrain social contagion. In Proc. 2012 International Conference on Privacy, Security, Risk and Trust and 2012 International Conference on Social Computing 249–257 (IEEE, 2012).

  46. 46.

    Lerman, K. Information is not a virus, and other consequences of human cognitive limits. Future Internet 8, 21 (2016).

    Google Scholar 

  47. 47.

    Muchnik, L. et al. Origins of power-law degree distribution in the heterogeneity of human activity in social networks. Sci. Rep. 3, 1783 (2013).

    CAS  Google Scholar 

  48. 48.

    Barabási, A. L. The origin of bursts and heavy tails in human dynamics. Nature 435, 207–211 (2005).

    Google Scholar 

  49. 49.

    Akbarpour, M. & Jackson, M. O. Diffusion in networks and the virtue of burstiness. Proc. Natl Acad. Sci. USA 115, E6996–E7004 (2018).

    CAS  Google Scholar 

  50. 50.

    Goldenberg, J., Han, S., Lehmann, D. R. & Hong, J. W. The role of hubs in the adoption process. J. Mark. 73, 1–13 (2009).

    Google Scholar 

  51. 51.

    Mønsted, B., Sapieżyński, P., Ferrara, E. & Lehmann, S. Evidence of complex contagion of information in social media: an experiment using Twitter bots. PLoS ONE 12, e0184148 (2017).

    Google Scholar 

  52. 52.

    Weng, L., Menczer, F. & Ahn, Y. Y. Virality prediction and community structure in social networks. Sci. Rep. 3, 2522 (2013).

    Google Scholar 

  53. 53.

    Cheng, J., Adamic, L., Dow, P. A., Kleinberg, J. M. & Leskovec, J. Can cascades be predicted? In Proc. 23rd International Conference on World Wide Web 925–936 (ACM, 2014).

  54. 54.

    Pei, S., Muchnik, L., Andrade, J. S. Jr, Zheng, Z. & Makse, H. A. Searching for superspreaders of information in real-world social media. Sci. Rep. 4, 5547 (2014).

    CAS  Google Scholar 

  55. 55.

    Efron, B. & Tibshirani, R. J. An Introduction to the Bootstrap (CRC Press, 1994).

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Acknowledgements

B.Z. is funded by Natural Science Foundation of China (grant no. 61503159) and Jiangsu University Overseas Training Programme. S.P. is supported by NIH NIGMS grant no. 5U01GM110748. L.M. is supported by Israel Science Foundation grant no. 1777/17. X.M. and H.E.S. are supported by NSF Grant PHY-1505000 and DTRA grant no. HDTRA-1-14-1-0017. X.X. is supported by National Natural Science Foundation of China (grant no. 61773091). A.S. wishes to thank the Ariel Cyber Innovation Centre in conjunction with the Israel National directorate in the Prime Minister’s Office for their support. S.H. thanks the Italian Ministry of Foreign Affairs and International Cooperation jointly with the Israeli Ministry of Science, Technology, and Space (MOST); the Israel Science Foundation, ONR, the Japan Science Foundation with MOST, BSF-NSF, ARO, the Bar-Ilan University Centre for Research in Applied Cryptography and Cyber Security and DTRA (grant no. HDTRA-1-19-1-0016) for financial support. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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All authors designed the research. B.Z. and S.P. performed the experiments and analysis. B.Z., S.P. and L.M. curated data. B.Z., S.P. and L.M. wrote the first draft of the manuscript. X.M., X.X., A.S., S.H. and H.E.S. reviewed and edited the manuscript.

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Correspondence to Bin Zhou or Sen Pei.

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Zhou, B., Pei, S., Muchnik, L. et al. Realistic modelling of information spread using peer-to-peer diffusion patterns. Nat Hum Behav 4, 1198–1207 (2020). https://doi.org/10.1038/s41562-020-00945-1

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