Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

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

Nature Human Behaviour volume 4, pages 1198–1207 (2020)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

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

    Google Scholar 

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

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

    Google Scholar 

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

    CAS  Google Scholar 

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

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

Download references

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.

Author information

Author notes

  1. These authors contributed equally: Bin Zhou, Sen Pei.

Authors and Affiliations

  1. School of Economics and Management, Jiangsu University of Science and Technology, Zhenjiang, China

    Bin Zhou

  2. Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, USA

    Bin Zhou, Xiangyi Meng, Shlomo Havlin & H. Eugene Stanley

  3. Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY, USA

    Sen Pei

  4. School of Business Administration, The Hebrew University of Jerusalem, Jerusalem, Israel

    Lev Muchnik

  5. Microsoft Research Israel, Alan Turing 3, Hertzliya, Israel

    Lev Muchnik

  6. College of Information and Communication Engineering, Dalian Minzu University, Dalian, China

    Xiaoke Xu

  7. Industrial Engineering Department, Ariel University, Ariel, Israel

    Alon Sela

  8. Department of Physics, Bar-Ilan University, Ramat Gan, Israel

    Shlomo Havlin

Authors
  1. Bin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sen Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lev Muchnik
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiangyi Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiaoke Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Alon Sela
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Shlomo Havlin
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. H. Eugene Stanley
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding authors

Correspondence to Bin Zhou or Sen Pei.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Primary handling editor: Aisha Bradshaw.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Tables 1–7 and Supplementary Figs. 1–8.

Reporting Summary

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41562-020-00945-1

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing