Don’t Be Greedy: Leveraging Community Structure to Find High Quality Seed Sets for Influence Maximization

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10660)


We consider the problem of maximizing the spread of influence in a social network by choosing a fixed number of initial seeds — a central problem in the study of network cascades. The majority of existing work on this problem, formally referred to as the influence maximization problem, is designed for submodular cascades. Despite the empirical evidence that many cascades are non-submodular, little work has been done focusing on non-submodular influence maximization.

We propose a new heuristic for solving the influence maximization problem and show via simulations on real-world and synthetic networks that our algorithm outputs more influential seed sets than the state-of-the-art greedy algorithm in many natural cases, with average improvements of 7% for submodular cascades, and 55% for non-submodular cascades. Our heuristic uses a dynamic programming approach on a hierarchical decomposition of the social network to leverage the relation between the spread of cascades and the community structure of social networks. We present “worst-case” theoretical results proving that in certain settings our algorithm outputs seed sets that are a factor of \(\varTheta (\sqrt{n})\) more influential than those of the greedy algorithm, where n is the number of nodes in the network.


  1. 1.
    Arora, S., Ge, R., Sachdeva, S., Schoenebeck, G.: Finding overlapping communities in social networks: toward a rigorous approach. In: ACM EC 2012 (2012)Google Scholar
  2. 2.
    Arthur, W.B.: Competing technologies, increasing returns, and lock-in by historical events. Econ. J. 99(394), 116–131 (1989). CrossRefGoogle Scholar
  3. 3.
    Backstrom, L., Huttenlocher, D.P., Kleinberg, J.M., Lan, X.: Group formation in large social networks: membership, growth, and evolution. In: KDD 2006, pp. 44–54 (2006)Google Scholar
  4. 4.
    Banerjee, A., Chandrasekhar, A.G., Duflo, E., Jackson, M.O.: The diffusion of microfinance. Science, 341(6144) (2013)Google Scholar
  5. 5.
    Borgs, C., Brautbar, M., Chayes, J.T., Lucier, B.: Maximizing social influence in nearly optimal time. In: SODA 2014 (2014)Google Scholar
  6. 6.
    Brown, J.J., Reingen, P.H.: Social ties and word-of-mouth referral behavior. J. Consum. Res. 14, 350–362 (1987)CrossRefGoogle Scholar
  7. 7.
    Centola, D.: The spread of behavior in an online social network experiment. Science 329(5996), 1194–1197 (2010)CrossRefGoogle Scholar
  8. 8.
    Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. In: KDD 2009. ACM (2009)Google Scholar
  9. 9.
    Chen, W., Yuan, Y., Zhang, L.: Scalable influence maximization in social networks under the linear threshold model. In: ICDM 2010, pp. 88–97. IEEE (2010)Google Scholar
  10. 10.
    Clauset, A., Newman, M.E., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70(6), 066111 (2004)CrossRefGoogle Scholar
  11. 11.
    Cohen, E., Delling, D., Pajor, T., Werneck, R.F.: Sketch-based influence maximization and computation: scaling up with guarantees. In: CIKM 2014, pp. 629–638. ACM (2014)Google Scholar
  12. 12.
    Coleman, J., Katz, E., Menzel, H.: The diffusion of an innovation among physicians. Sociometry 20, 253–270 (1957)CrossRefGoogle Scholar
  13. 13.
    Conley, T.G., Udry, C.R.: Learning about a new technology: pineapple in Ghana. Am. Econ. Rev. 100(1), 35–69 (2010)CrossRefGoogle Scholar
  14. 14.
    Cordasco, G., Gargano, L., Mecchia, M., Rescigno, A.A., Vaccaro, U.: Discovering small target sets in social networks: a fast and effective algorithm. arXiv preprint arXiv:1610.03721 (2016)
  15. 15.
    Dasgupta, S.: A cost function for similarity-based hierarchical clustering. In: STOC 2016, pp. 118–127. ACM, New York, NY, USA (2016).
  16. 16.
    Domingos, P., Richardson, M.: Mining the network value of customers. In: 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 57–66 (2001)Google Scholar
  17. 17.
    Goyal, A., Lu, W., Lakshmanan, L.V.: Celf++: optimizing the greedy algorithm for influence maximization in social networks. In: WWW 2011. pp. 47–48. ACM (2011)Google Scholar
  18. 18.
    Goyal, A., Lu, W., Lakshmanan, L.V.: Simpath: an efficient algorithm for influence maximization under the linear threshold model. In: ICDM 2011, pp. 211–220. IEEE (2011)Google Scholar
  19. 19.
    Goyal, S., Kearns, M.: Competitive contagion in networks. In: STOC 2012, pp. 759–774 (2012)Google Scholar
  20. 20.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978). CrossRefGoogle Scholar
  21. 21.
    Karypis, G., Kumar, V.: METIS: unstructured graph partitioning and sparse matrix ordering system, Version 4.0. (2009).
  22. 22.
    Kempe, D., Kleinberg, J.M., Tardos, É.: Maximizing the spread of influence through a social network. In: KDD 2003, pp. 137–146 (2003)Google Scholar
  23. 23.
    Kempe, D., Kleinberg, J., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005). CrossRefGoogle Scholar
  24. 24.
    Kimura, M., Saito, K.: Tractable models for information diffusion in social networks. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS, vol. 4213, pp. 259–271. Springer, Heidelberg (2006). CrossRefGoogle Scholar
  25. 25.
    Kleinberg, J.: Small-world phenomena and the dynamics of information. In: NIPS 2002, vol. 1, pp. 431–438 (2002)Google Scholar
  26. 26.
    Lerman, K., Ghosh, R.: Information contagion: an empirical study of the spread of news on Digg and Twitter social networks. ICWSM 10, 90–97 (2010)Google Scholar
  27. 27.
    Leskovec, J., Adamic, L.A., Huberman, B.A.: The dynamics of viral marketing. In: ACM EC 2006, pp. 228–237 (2006)Google Scholar
  28. 28.
    Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., Glance, N.: Cost-effective outbreak detection in networks. In: KDD 2007, pp. 420–429. ACM (2007)Google Scholar
  29. 29.
    Leskovec, J., Krevl, A.: SNAP datasets: stanford large network dataset collection, June 2014.
  30. 30.
    Lucier, B., Oren, J., Singer, Y.: Influence at scale: distributed computation of complex contagion in networks. In: KDD 2015, pp. 735–744. ACM (2015)Google Scholar
  31. 31.
    Morris, S.: Contagion. Rev. Econ. Stud. 67(1), 57–78 (2000). MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Mossel, E., Roch, S.: Submodularity of influence in social networks: from local to global. SIAM J. Comput. 39(6), 2176–2188 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Nguyen, H., Zheng, R.: Influence spread in large-scale social networks – a belief propagation approach. In: Flach, P.A., De Bie, T., Cristianini, N. (eds.) ECML PKDD 2012. LNCS, vol. 7524, pp. 515–530. Springer, Heidelberg (2012). CrossRefGoogle Scholar
  34. 34.
    Paluck, E.L., Shepherd, H., Aronow, P.M.: Changing climates of conflict: a social network experiment in 56 schools. Proc. Nat. Acad. Sci. 113(3), 566–571 (2016). CrossRefGoogle Scholar
  35. 35.
    Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: KDD 2012, pp. 61–70 (2002)Google Scholar
  36. 36.
    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: WWW 2011. pp. 695–704. ACM (2011).
  37. 37.
    Schoenebeck, G., Tao, B.: Beyond worst-case (in)approximability of nonsubmodular influence maximization (2017).
  38. 38.
    Seeman, L., Singer, Y.: Adaptive seeding in social networks. In: FOCS 2013, pp. 459–468. IEEE (2013)Google Scholar
  39. 39.
    Tang, Y., Xiao, X., Shi, Y.: Influence maximization: near-optimal time complexity meets practical efficiency. In: Proceedings of the 2014 ACM SIGMOD International Conference on Management of Data, pp. 75–86. ACM (2014)Google Scholar
  40. 40.
    Tullock, G.: Towards a theory of the rent-seeking society. In: chap. Efficient Rent Seeking. Texas A&M University Press (1980)Google Scholar
  41. 41.
    Wang, Y., Cong, G., Song, G., Xie, K.: Community-based greedy algorithm for mining top-k influential nodes in mobile social networks. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1039–1048. ACM (2010)Google Scholar
  42. 42.
    Watts, D.J.: A simple model of global cascades on random networks. Proc. Nat. Acad. Sci. 99(9), 5766–5771 (2002). MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of MassachusettsAmherstUSA
  2. 2.University of MichiganAnn ArborUSA

Personalised recommendations