Anomalous structure and dynamics in news diffusion among heterogeneous individuals

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Previous research has suggested that well-connected nodes in a network (commonly referred to as hubs) are better at spreading information than those with fewer connections (ordinary users). Here we investigate the roles of nodes with different numbers of connections by studying how people share news online. Quantitative analysis shows that users without many connections can sometimes spread news more effectively than well-connected users when the diffusion pattern has dendrite-like paths that reach far into the network, leading to a non-Gaussian distance distribution. When the hubs dominate, however, the distribution is Gaussian. Enhanced interactions among ordinary users are the key to the emergence of non-Gaussian characteristics. Finally, we introduce a message-passing model that reproduces the observed diffusion features. This model shows that patterns dominated by either hubs or ordinary users can be clearly demarcated by measuring the average number of forwards.

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Fig. 1: Measuring the direction of information flow.
Fig. 2: Roles of the two types of users in real-world message spreading.
Fig. 3: Structure of news diffusion networks.
Fig. 4: Illustration of the message-passing model with heterogeneous influence strength.
Fig. 5: Reproducing the spreading patterns of news1, news2 and news3.
Fig. 6: Diffusion networks produced by the model.
Fig. 7: Parameter dependence of the diffusion network structure and diffusion patterns.

Data availability

The headlines of all the news stories were collected from the hot news website of Sina News Center ( We asked a commercial institution ( to help us collect data on Sina Weibo ( The downloaded data include all the posts for each piece of news (that is, their respective user interactions and the follower counts of the users) that are publicly available on Sina Weibo (users with privacy restrictions are not included in the dataset). The data that support the findings of this study are available at

Code availability

Code for the data analysis and model simulation is available at The code was run using Python 238 and Matlab R2015b39 for data analysis and Matlab R2015b for model simulation.


  1. 1.

    Granovetter, M. Threshold models of collective behavior. Am. J. Sociol. 83, 1420–1443 (1978).

  2. 2.

    Christakis, N. A. & Fowler, J. H. The spread of obesity in a large social network over 32 years. N. Engl. J. Med. 357, 370–379 (2007).

  3. 3.

    Christakis, N. A. & Fowler, J. H. The collective dynamics of smoking in a large social network. N. Engl. J. Med. 358, 2249–2258 (2008).

  4. 4.

    Fowler, J. H. & Christakis, N. A. Dynamic spread of happiness in a large social network: longitudinal analysis over 20 years in the Framingham Heart Study. BMJ 337, a2338 (2008).

  5. 5.

    Barrat, A., Barthélemy, M. & Vespignani, A. Dynamical Processes on Complex Networks (Cambridge Univ. Press, 2008).

  6. 6.

    Fowler, J. H. & Christakis, N. A. Cooperative behavior cascades in human social networks. Proc. Natl Acad. Sci. USA 107, 5334–5338 (2010).

  7. 7.

    Lazarsfeld, P. F., Berelson, B. & Gaudet, H. The People’s Choice: How the Voter Makes Up His Mind in a Presidential Campaign (Columbia Univ. Press, 1948).

  8. 8.

    Katz, E. & Lazarsfeld, P. F. Personal Influence (Free Press, 1955).

  9. 9.

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

  10. 10.

    Wang, W., Tang, M., Shu, P. P. & Wang, Z. Dynamics of social contagions with heterogeneous adoption thresholds: crossover phenomena in phase transition. New J. Phys. 18, 013029 (2016).

  11. 11.

    Lee, E. & Holme, P. Social contagion with degree-dependent thresholds. Phys. Rev. E 96, 012315 (2017).

  12. 12.

    Yang, W., Cao, L., Wang, X. F. & Li, X. Consensus in a heterogeneous influence network. Phys. Rev. E 74, 037101 (2006).

  13. 13.

    Lin, Y. T., Yang, H. X., Rong, Z. H. & Wang, B. H. Effects of heterogeneous influence of individuals on the global consensus. Int. J. Mod. Phys. C 21, 1011–1019 (2010).

  14. 14.

    Xiong, F., Liu, Y. & Zhu, J. Competition of dynamic self-confidence and inhomogeneous individual influence in voter models. Entropy 15, 5292–5304 (2013).

  15. 15.

    Liang, H. L., Yang, Y. P. & Wang, X. F. Opinion dynamics in networks with heterogeneous confidence and influence. Physica A 392, 2248–2256 (2013).

  16. 16.

    Schmidt, A. L. et al. Anatomy of news consumption on Facebook. Proc. Natl Acad. Sci. USA 114, 3035–3039 (2017).

  17. 17.

    Deffuant, G., Neau, D., Amblard, F. & Weisbuch, G. Mixing beliefs among interacting agents. Adv. Complex Syst. 3, 87–98 (2000).

  18. 18.

    Del Vicario, M. et al. The spreading of misinformation online. Proc. Natl Acad. Sci. USA 113, 554–559 (2016).

  19. 19.

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

  20. 20.

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

  21. 21.

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

  22. 22.

    Onnela, J. P. & Reed-Tsochas, F. Spontaneous emergence of social influence in online systems. Proc. Natl Acad. Sci. USA 107, 18375–18380 (2010).

  23. 23.

    Zheng, M. H., Lü, L. Y. & Zhao, M. Spreading in online social networks: the role of social reinforcement. Phys. Rev. E 88, 012818 (2013).

  24. 24.

    Centola, D. How Behavior Spreads: the Science of Complex Contagions (Princeton Univ. Press, 2018).

  25. 25.

    Romero, D. M., Meeder, B. & Kleinberg, J. Differences in the mechanics of information diffusion across topics: idioms, political hashtags, and complex contagion on twitter. In Proc. 20th International Conference on World Wide Web 695−704 (ACM, 2011).

  26. 26.

    Borge-Holthoefer, J. et al. The dynamics of information-driven coordination phenomena: a transfer entropy analysis. Sci. Adv. 2, e1501158 (2016).

  27. 27.

    Wang, W., Tang, M., Zhang, H. F. & Lai, Y. C. Dynamics of social contagions with memory of nonredundant information. Phys. Rev. E 92, 012820 (2015).

  28. 28.

    Wang, W., Shu, P. P., Zhu, Y. X., Tang, M. & Zhang, Y. C. Dynamics of social contagions with limited contact capacity. Chaos 25, 103102 (2015).

  29. 29.

    Pathria, R. K. Statistical Mechanics (Elsevier, 2005).

  30. 30.

    Bouchaud, J.-P. & Georges, A. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195, 127–293 (1990).

  31. 31.

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

  32. 32.

    Roch, C. H. The dual roots of opinion leadership. J. Polit. 67, 110–131 (2005).

  33. 33.

    Freeman, L. C. Centrality in social networks conceptual clarification. Soc. Networks 1, 215–239 (1979).

  34. 34.

    Friedkin, N. E. Theoretical foundations for centrality measures. Am. J. Sociol. 96, 1478–1504 (1991).

  35. 35.

    Bonacich, P. Power and centrality: a family of measures. Am. J. Sociol. 92, 1170–1182 (1987).

  36. 36.

    Albert, R. & Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002).

  37. 37.

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

  38. 38.

    Hetland, M. L. Beginning Python: from Novice to Professional 2nd ed. (Apress, 2008).

  39. 39.

    Chapman S. J. Essentials of Matlab Programming 2nd ed., (Cengage Learning, 2008).

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This work was supported by the National Natural Science Foundation of China (grant nos. 11775034 and 11375093). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

X.W., Y.L. and J.X. contributed equally to all parts of the research and writing.

Correspondence to Xiaochen Wang or Jinghua Xiao.

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The authors declare no competing interests.

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Supplementary Information

Supplementary Methods 1−8, Supplementary Notes 1−5, Supplementary Tables 1−6, Supplementary Figures 1−17 and Supplementary References.

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Wang, X., Lan, Y. & Xiao, J. Anomalous structure and dynamics in news diffusion among heterogeneous individuals. Nat Hum Behav 3, 709–718 (2019) doi:10.1038/s41562-019-0605-7

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