Inferring networks of diffusion and influence

ABSTRACT

Information diffusion and virus propagation are fundamental processes talking place in networks. While it is often possible to directly observe when nodes become infected, observing individual transmissions (i.e., who infects whom or who influences whom) is typically very difficult. Furthermore, in many applications, the underlying network over which the diffusions and propagations spread is actually unobserved. We tackle these challenges by developing a method for tracing paths of diffusion and influence through networks and inferring the networks over which contagions propagate. Given the times when nodes adopt pieces of information or become infected, we identify the optimal network that best explains the observed infection times. Since the optimization problem is NP-hard to solve exactly, we develop an efficient approximation algorithm that scales to large datasets and in practice gives provably near-optimal performance. We demonstrate the effectiveness of our approach by tracing information cascades in a set of 170 million blogs and news articles over a one year period to infer how information flows through the online media space. We find that the diffusion network of news tends to have a core-periphery structure with a small set of core media sites that diffuse information to the rest of the Web. These sites tend to have stable circles of influence with more general news media sites acting as connectors between them.

References

1. Supporting website. http://snap.stanford.edu/netinf.
2. . Adar and L. A. Adamic. Tracking information epidemics in blogspace. In Web Intelligence, pages 207--214, 2005.
3. .-L. Barabási. The origin of bursts and heavy tails in human dynamics. Nature, 435:207, 2005.
4. .-L. Barabási and R. Albert. Emergence of scaling in random networks. Science, 286:509--512, 1999.
5. . Clauset, C. Moore, and M. E. J. Newman. Hierarchical structure and the prediction of missing links in networks. Nature, 453(7191):98--101, 2008.
6. . Crane and D. Sornette. Robust dynamic classes revealed by measuring the response function of a social system. Proc. of the National Academy of Sciences, 105(41):15649--15653, October 2008.
7. . Edmonds. Optimum branchings. Journal of Resesearch of the National Bureau of Standards, (71B):233--240, 1967.
8. . Erd\Hos and A. Rényi. On the evolution of random graphs. Publication of the Mathematical Institute of the Hungarian Academy of Science, 5:17--67, 1960.
9. . Friedman and D. Koller. Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Machine Learning, 50(1):95--125, 2003.
10. . Friedman, I. Nachman, and D. Pe'er. Learning Bayesian network structure from massive datasets: The "Sparse Candidate" algorithm. In Proc. UAI, 1999.
11. . Gruhl, R. Guha, D. Liben-Nowell, and A. Tomkins. Information diffusion through blogspace. In WWW '04: Proc. of the 13th international conference on World Wide Web, pages 491--501, 2004.
12. . Katz and P. Lazarsfeld. Personal influence: The part played by people in the flow of mass communications. Free Press, 1955.
13. . Kempe, J. M. Kleinberg, and E. Tardos. Maximizing the spread of influence through a social network. In KDD '03: Proc. of the 9th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 137--146, 2003.
14. . Khuller, A. Moss, and J. Naor. The budgeted maximum coverage problem. Information Processing Letters, 70(1):39--45, 1999.
15. . Knuth. The art of computer programming. Addison-Wesley, 1968.
16. . Kumar, J. Novak, P. Raghavan, and A. Tomkins. Structure and evolution of blogspace. CACM, 47(12):35--39, 2004.
17. . Leskovec, L. A. Adamic, and B. A. Huberman. The dynamics of viral marketing. In EC '06: Proc. of the 7th ACM conference on Electronic commerce, pages 228--237, 2006.
18. . Leskovec, L. Backstrom, and J. Kleinberg. Meme-tracking and the dynamics of the news cycle. In KDD '09: Proc. of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 497--506, New York, NY, USA, 2009. ACM.
19. . Leskovec and C. Faloutsos. Scalable modeling of real graphs using kronecker multiplication. In ICML '07: Proc. of the 24th International Conference on Machine Learning, page 504, 2007.
20. . Leskovec, J. Kleinberg, and C. Faloutsos. Graphs over time: densification laws, shrinking diameters and possible explanations. In KDD '05: Proc. of the 11th ACM SIGKDD international conference on Knowledge discovery in data mining, page 187, 2005.
21. . Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. VanBriesen, and N. Glance. Cost-effective outbreak detection in networks. In KDD '07: Proc. of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 420--429, 2007.
22. . Leskovec, K. J. Lang, A. Dasgupta, and M. W. Mahoney. Statistical properties of community structure in large social and information networks. In WWW '08: Proc. of the 17th International Conference on World Wide Web, 2008.
23. . Leskovec, M. McGlohon, C. Faloutsos, N. Glance, and M. Hurst. Cascading behavior in large blog graphs. In SDM '07: Proc. of the SIAM Conference on Data Mining, 2007.
24. . Leskovec, A. Singh, and J. M. Kleinberg. Patterns of influence in a recommendation network. In PAKDD '06: Proc. of the 10th Pacific-Asia Conference on Knowledge Discovery and Data Mining, pages 380--389, 2006.
25. . Liben-Nowell and J. Kleinberg. Tracing the flow of information on a global scale using Internet chain-letter data. Proc. of the National Academy of Sciences, 105(12):4633--4638, 25 Mar. 2008.
26. . D. Malmgren, D. B. Stouffer, A. E. Motter, and L. A. A. N. Amaral. A poissonian explanation for heavy tails in e-mail communication. Proc. of the National Academy of Sciences, 105(47):18153--18158, November 2008.
27. . Nemhauser, L. Wolsey, and M. Fisher. An analysis of approximations for maximizing submodular set functions. Mathematical Programming, 14(1):265--294, 1978.
28. . M. Rogers. Diffusion of Innovations. Free Press, New York, fourth edition, 1995.
29. . Wallinga and P. Teunis. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. American Journal of Epidemiology, 160(6):509--516, 2004.
30. . J. Watts and P. S. Dodds. Influentials, networks, and public opinion formation. Journal of Consumer Research, 34(4):441--458, December 2007.

Index Terms

• Information systems

  • Information systems applications

    • Data mining