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.

  • Letter
  • Published:

Social influence maximization under empirical influence models

Nature Human Behaviour volume 2, pages 375–382 (2018)Cite this article

Subjects

A Publisher Correction to this article was published on 02 August 2018

This article has been updated

Abstract

Social influence maximization models aim to identify the smallest number of influential individuals (seed nodes) that can maximize the diffusion of information or behaviours through a social network. However, while empirical experimental evidence has shown that network assortativity and the joint distribution of influence and susceptibility are important mechanisms shaping social influence, most current influence maximization models do not incorporate these features. Here, we specify a class of empirically motivated influence models and study their implications for influence maximization in six synthetic and six real social networks of varying sizes and structures. We find that ignoring assortativity and the joint distribution of influence and susceptibility leads traditional models to underestimate influence propagation by 21.7% on average, for a fixed seed set size. The traditional models and the empirical types that we specify here also identify substantially different seed sets, with only 19.8% overlap between them. The optimal seeds chosen under empirical influence models are relatively less well-connected and less central nodes, and they have more cohesive, embedded ties with their contacts. Hence, empirically motivated influence models have the potential to identify more realistic sets of key influencers in a social network and inform intervention designs that disseminate information or change attitudes and behaviours.

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: Parameterization of influence and susceptibility and implications for seed set selection.
Fig. 2: Influence diffusion under identical influence maximization regimes with different influence models.
Fig. 3: Influence diffusion under identical influence maximization regimes with different influence models.
Fig. 4: Overlap among and structural differences between seed sets under different influence models.

Similar content being viewed by others

Change history

  • 02 August 2018

    In the version of this Letter originally published, in the key for Fig. 1 the red square was mistakenly labelled ‘Low influence’ and ‘High susceptibility’ but should have been labelled ‘High influence’ and ‘Low susceptibility’. This has now been corrected.

References

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

    Article  CAS  Google Scholar 

  2. Banerjee, A., Chandrasekhar, A., Duflo, E. & Jackson, M. The diffusion of microfinance. Science 341, 1236498 (2013).

    Article  PubMed  CAS  Google Scholar 

  3. 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 (2003).

  4. Kempe, D., Kleinberg, J. & Tardos, É. Maximizing the spread of influence through a social network. Theory Comput. 11, 105–147 (2015).

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Bakshy, E., Rosenn, I., Marlow, C. & Adamic, L. The role of social networks in information diffusion. In Proc. 21st International Conference on World Wide Web 519–528 (2012).

  7. Centola, D., Eguiluz, V. & Macy, M. Cascade dynamics of complex propagation. Physica A 374, 449–456 (2007).

    Article  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  9. 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 (2001).

  10. van den Bulte, C. & Joshi, Y. New product diffusion with influentials and imitators. Mark. Sci. 26, 400–421 (2007).

    Article  Google Scholar 

  11. Altarelli, F. et al. Containing epidemic outbreaks by message-passing techniques. Phys. Rev. X 4, 021024 (2014).

    Google Scholar 

  12. Newman, M. Spread of epidemic disease on networks. Phys. Rev. E 66, 016128 (2002).

    Article  CAS  Google Scholar 

  13. Chen, Y. et al. Finding a better immunization strategy. Phys. Rev. Lett. 101, 058701 (2008).

    Article  PubMed  CAS  Google Scholar 

  14. Kawachi, I. & Berkman, L. Social ties and mental health. J. Urban Health 78, 458–467 (2001).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  15. van Leeuwen, J. Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity (MIT Press, Cambridge, MA, 1991).

  16. Chen, W., Wang, Y. & Yang, S. Efficient influence maximization in social networks. In Proc. 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 199–208 (2009).

  17. Wang, C., Chen, W. & Wang, Y. Scalable influence maximization for independent cascade model in large-scale social networks. Data Min. Knowl. Discov. 25, 545–576 (2012).

    Article  Google Scholar 

  18. Borges, C., Brautbar, M., Chayes, J. & Lucier, B. Maximizing social influence in nearly optimal time. In Proc. 25th Annual ACM-SIAM Symposium on Discrete Algorithms 946–957 (2014).

  19. Leskovec, J. et al. Cost-effective outbreak detection in networks. In Proc. 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 420–429 (2007).

  20. Goyal, A., Lu, W. & Laksmanan, L. Celf++: optimizing the greedy algorithm for influence maximization in social networks. In Proc. 20th International Conference Companion on World Wide Web 47–48 (2011).

  21. Tang, Y., Xiaokui, X. & Shi, Y. Influence maximization: near-optimal time complexity meets practical efficiency. In Proc. 2014 ACM SIGMOD International Conference on Management of Data 75–86 (2014).

  22. He, X. & Kempe, D. Robust influence maximization. In Proc. 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 885–894 (2016).

  23. Chen, W., Lin, T., Tan, Z., Zhao, M. & Zhou, X. Robust influence maximization. In Proc. 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 795–804 (2016).

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

    Article  Google Scholar 

  25. 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).

    Article  Google Scholar 

  26. Goldenberg, J., Libai, B. & Muller, E. Using complex systems analysis to advance marketing theory development: modeling heterogeneity effects on new product growth through stochastic cellular automata. Acad. Mark. Sci. Rev. 9, 1–18 (2001).

    Google Scholar 

  27. Gomez-Rodriguez, M. et al. Influence estimation and maximization in continuous-time diffusion networks. ACM Trans. Inf. Syst. 34, 9 (2016).

    Article  Google Scholar 

  28. Morone, F. & Makse, H. A. Influence maximization in complex networks through optimal percolation. Nature 524, 65–68 (2015).

    Article  PubMed  CAS  Google Scholar 

  29. Newman, M. Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002).

    Article  PubMed  CAS  Google Scholar 

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

    Article  Google Scholar 

  31. Bramoullé, Y., Djebbari, H. & Fortin, B. Identification of peer effects through social networks. J. Econ. 150, 41–55 (2009).

    Article  Google Scholar 

  32. Golub, B. & Jackson, M. O. How homophily affects the speed of learning and best-response dynamics. Q. J. Econ. 127, 1287–1338 (2012).

    Article  Google Scholar 

  33. Aral, S., Muchnik, L. & Sundararajan, A. Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks. Proc. Natl Acad. Sci. USA 106, 21544–21549 (2009).

    Article  PubMed  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  35. Bakshy, E., Hofman, J., Mason, W. & Watts, D. Everyone's an influencer: quantifying influence on twitter. In Proc. 4th ACM International Conference on Web Search and Data Mining 65–74 (2011).

  36. Burt, R. Structural holes and good ideas. Am. J. Sociol. 110, 349–399 (2004).

    Article  Google Scholar 

  37. Aral, S. Commentary-identifying social influence: a comment on opinion leadership and social contagion in new product diffusion. Mark. Sci. 30, 217–223 (2011).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  40. Bakshy, E., Eckles, D. & Bernstein, M. Designing and deploying online field experiments. In Proc. 23rd International Conference on World Wide Web 283–292 (2014).

  41. Aral, S. & Walker, D. Tie strength, embeddedness, and social influence: a large-scale networked experiment. Manage. Sci. 60, 1352–1370 (2014).

    Article  Google Scholar 

  42. Ugander, J. & Backstrom, L. Balanced label propagation for partitioning massive graphs. In Proc. 6th ACM International Conference on Web Search and Data Mining 507–516 (2013).

  43. Pfeiffer, J. III et al. Attributed graph models: modeling network structure with correlated attributes. In Proc. 23rd International Conference on World Wide Web 831–842 (2014).

Download references

Acknowledgements

We thank to D. Eckles for invaluable discussions. S.A. acknowledges funding and support from the NSF (Career Award 0953832). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Authors and Affiliations

  1. MIT Sloan School of Management, Cambridge, MA, USA

    Sinan Aral & Paramveer S. Dhillon

Authors
  1. Sinan Aral
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paramveer S. Dhillon
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.A. and P.S.D. contributed equally to all parts of the research and writing.

Corresponding authors

Correspondence to Sinan Aral or Paramveer S. Dhillon.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Methods, Supplementary Note 1, Supplementary Figures 1–58

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aral, S., Dhillon, P.S. Social influence maximization under empirical influence models. Nat Hum Behav 2, 375–382 (2018). https://doi.org/10.1038/s41562-018-0346-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41562-018-0346-z

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