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Theories for Influencer Identification in Complex Networks

  • Sen Pei
  • Flaviano Morone
  • Hernán A. Makse
Chapter
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Abstract

In social and biological systems, the structural heterogeneity of interaction networks gives rise to the emergence of a small set of influential nodes, or influencers, in a series of dynamical processes. Although much smaller than the entire network, these influencers were observed to be able to shape the collective dynamics of large populations in different contexts. As such, the successful identification of influencers should have profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks, and cascading failure. In this chapter, we first summarize the centrality-based approach in finding single influencers in complex networks, and then discuss the more complicated problem of locating multiple influencers from a collective point of view. Progress rooted in collective influence theory, belief-propagation, and computer science will be presented. Finally, we present some applications of influencer identification in diverse real-world systems, including online social platforms, scientific publication, brain networks, and socioeconomic systems.

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Notes

Acknowledgements

We acknowledge funding from NIH-NIBIB 1R01EB022720, NIH-NCI U54CA137788 / U54CA132378 and NSF-IIS 1515022.

References

  1. 1.
    Albert R, Jeong H, Barabási AL (2000) Error and attack tolerance of complex networks. Nature 406(6794):378–382CrossRefADSGoogle Scholar
  2. 2.
    Altarelli F, Braunstein A, Dall’Asta L, Zecchina R (2013) Large deviations of cascade processes on graphs. Phys Rev E 87(6):062115Google Scholar
  3. 3.
    Altarelli F, Braunstein A, Dall’Asta L, Zecchina R (2013) Optimizing spread dynamics on graphs by message passing. J Stat Mech: Theory Exp 2013(09):P09011MathSciNetCrossRefGoogle Scholar
  4. 4.
    Altarelli F, Braunstein A, Dall’Asta L, Wakeling JR, Zecchina R (2014) Containing epidemic outbreaks by message-passing techniques. Phys Rev X 4(2):021024Google Scholar
  5. 5.
    Backstrom L, Huttenlocher D, Kleinberg J, Lan X (2006) Group formation in large social networks: membership, growth, and evolution. In: Proceedings of the 12th ACM SIGKDD international conference on knowledge discovery and data mining. Association for Computing Machinery, New York, pp 44–54Google Scholar
  6. 6.
    Bakshy E, Hofman JM, Mason WA, Watts DJ (2011) Everyone’s an influencer: quantifying influence on twitter. In: Proceeding of the 4th ACM international conference on web search and data mining. Association for Computing Machinery, New York, pp 65–74Google Scholar
  7. 7.
    Batagelj V, Zaversnik M (2003) An o (m) algorithm for cores decomposition of networks. arXiv preprint cs/0310049Google Scholar
  8. 8.
    Bau S, Wormald NC, Zhou S (2002) Decycling numbers of random regular graphs. Random Struct Algoritm 21(3–4):397–413Google Scholar
  9. 9.
    Baxter GJ, Dorogovtsev SN, Goltsev AV, Mendes JF (2010) Bootstrap percolation on complex networks. Phys Rev E 82(1):011103Google Scholar
  10. 10.
    Bonacich P (1972) Factoring and weighting approaches to status scores and clique identification. J Math Socio 2(1):113–120CrossRefGoogle Scholar
  11. 11.
    Borge-Holthoefer J, Moreno Y (2012) Absence of influential spreaders in rumor dynamics. Phys Rev E 85(2):026116Google Scholar
  12. 12.
    Braunstein A, Dall’Asta L, Semerjian G, Zdeborová L (2016) Network dismantling. Proc Natl Acad Sci U S A 113(44):12368–12373CrossRefGoogle Scholar
  13. 13.
    Brin S, Page L (1998) The anatomy of a large-scale hypertextual web search engine. Comput Netw ISDN Syst 30(1):107–117CrossRefGoogle Scholar
  14. 14.
    Buldyrev SV, Parshani R, Paul G, Stanley HE, Havlin S (2010) Catastrophic cascade of failures in interdependent networks. Nature 464(7291):1025–1028CrossRefADSGoogle Scholar
  15. 15.
    Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10(3):186–198CrossRefGoogle Scholar
  16. 16.
    Callaway DS, Newman ME, Strogatz SH, Watts DJ (2000) Network robustness and fragility: percolation on random graphs. Phys Rev Lett 85(25):5468CrossRefADSGoogle Scholar
  17. 17.
    Centola D (2010) The spread of behavior in an online social network experiment. Science 329(5996):1194–1197CrossRefADSGoogle Scholar
  18. 18.
    Cha M, Haddadi H, Benevenuto F, Gummadi PK (2010) Measuring user influence in twitter: the million follower fallacy. In: Proceeding of the 4th international AAAI conference on weblogs and social media 10(10–17):30Google Scholar
  19. 19.
    Chen W, Wang Y, Yang S (2009) Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD international conference on knowledge discovery and data mining. Association for Computing Machinery, New York, pp 199–208Google Scholar
  20. 20.
    Chen W, Wang C, Wang Y (2010) Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of the 16th ACM SIGKDD international conference on knowledge discovery and data mining. Association for Computing Machinery, New York, pp 1029–1038Google Scholar
  21. 21.
    Chen W, Yuan Y, Zhang L (2010) Scalable influence maximization in social networks under the linear threshold model. In: 2010 IEEE 10th international conference on data mining (ICDM). IEEE, Los Alamitos, CA, pp 88–97Google Scholar
  22. 22.
    Clusella P, Grassberger P, Pérez-Reche FJ, Politi A (2016) Immunization and targeted destruction of networks using explosive percolation. Phys Rev Lett 117(20):208301Google Scholar
  23. 23.
    Cohen R, Erez K, Ben-Avraham D, Havlin S (2001) Breakdown of the internet under intentional attack. Phys Rev Lett 86(16):3682CrossRefADSGoogle Scholar
  24. 24.
    Eagle N, Macy M, Claxton R (2010) Network diversity and economic development. Science 328(5981):1029–1031MathSciNetCrossRefADSzbMATHGoogle Scholar
  25. 25.
    Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1(3):215–239CrossRefGoogle Scholar
  26. 26.
    Gallos LK, Sigman M, Makse HA (2007) The conundrum of functional brain networks: small-world efficiency or fractal modularity. Front Psychol 3:123Google Scholar
  27. 27.
    Gallos LK, Song C, Makse HA (2008) Scaling of degree correlations and its influence on diffusion in scale-free networks. Phys Rev Lett 100(24):248701Google Scholar
  28. 28.
    Gallos LK, Makse HA, Sigman M (2012) A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. Proc Natl Acad Sci U S A 109(8):2825–2830CrossRefADSGoogle Scholar
  29. 29.
    Goltsev AV, Dorogovtsev SN, Mendes JFF (2006) k-core (bootstrap) percolation on complex networks: critical phenomena and nonlocal effects. Phys Rev E 73(5):056101Google Scholar
  30. 30.
    Goyal A, Lu W, Lakshmanan LV (2011) Celf++: optimizing the greedy algorithm for influence maximization in social networks. In: Proceedings of the 20th international conference on world wide web. Association for Computing Machinery, New York, pp 47–48Google Scholar
  31. 31.
    Goyal A, Lu W, Lakshmanan LV (2011) Simpath: an efficient algorithm for influence maximization under the linear threshold model. In: 2011 IEEE 11th international conference on data mining (ICDM). IEEE, Los Alamitos, CA, pp 211–220Google Scholar
  32. 32.
    Granovetter MS (1973) The strength of weak ties. Am J Sociol 78(6):1360–1380CrossRefGoogle Scholar
  33. 33.
    Guggiola A, Semerjian G (2015) Minimal contagious sets in random regular graphs. J Stat Phys 158(2):300–358MathSciNetCrossRefADSzbMATHGoogle Scholar
  34. 34.
    Hashimoto KI (1989) Zeta functions of finite graphs and representations of p-adic groups. Adv Stud Pure Math 15:211–280MathSciNetCrossRefGoogle Scholar
  35. 35.
    Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev 42(4):599–653MathSciNetCrossRefADSzbMATHGoogle Scholar
  36. 36.
    Hu Y, Havlin S, Makse HA (2014) Conditions for viral influence spreading through multiplex correlated social networks. Phys Rev X 4(2):021031Google Scholar
  37. 37.
    Hu Y, Ji S, Feng L, Havlin S, Jin Y (2015) Optimizing locally the spread of influence in large scale online social networks. arXiv preprint arXiv:1509.03484Google Scholar
  38. 38.
    Karp RM (1972) Reducibility among combinatorial problems. In: Complexity of computer computations. Springer, Berlin, pp 85–103CrossRefGoogle Scholar
  39. 39.
    Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1): 39–43CrossRefMathSciNetzbMATHGoogle Scholar
  40. 40.
    Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD international conference on knowledge discovery and data mining. Association for Computing Machinery, New York, pp 137–146Google Scholar
  41. 41.
    Kitsak M, Gallos LK, Havlin S, Liljeros F, Muchnik L, Stanley HE, Makse HA (2010) Identification of influential spreaders in complex networks. Nat Phys 6(11):888–893CrossRefGoogle Scholar
  42. 42.
    Kleinberg J (2007) Cascading behavior in networks: algorithmic and economic issues. Algorithmic Game Theory 24:613–632MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Klemm K, Serrano M, Eguiluz VM, Miguel MS (2012) A measure of individual role in collective dynamics. Sci Rep 2:292CrossRefADSGoogle Scholar
  44. 44.
    Kwak H, Lee C, Park H, Moon S (2010) What is twitter, a social network or a news media? In: Proceeding of the 19th ACM international conference on world wide web. Association for Computing Machinery, New York, pp 591–600Google Scholar
  45. 45.
    Lawyer G (2015) Understanding the influence of all nodes in a network. Sci Rep 5:8665CrossRefADSGoogle Scholar
  46. 46.
    Leskovec J, Adamic LA, Huberman BA (2007) The dynamics of viral marketing. ACM Trans Web 1(1):5CrossRefGoogle Scholar
  47. 47.
    Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen J, Glance N (2007) Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD international conference on knowledge discovery and data mining. Association for Computing Machinery, New York, pp 420–429CrossRefGoogle Scholar
  48. 48.
    Li W, Tang S, Pei S, Yan S, Jiang S, Teng X, Zheng Z (2014) The rumor diffusion process with emerging independent spreaders in complex networks. Physica A 397:121–128MathSciNetCrossRefADSzbMATHGoogle Scholar
  49. 49.
    Liben-Nowell D, Kleinberg J (2008) Tracing information flow on a global scale using internet chain-letter data. Proc Natl Acad Sci U S A 105(12):4633–4638CrossRefADSGoogle Scholar
  50. 50.
    Liu Y, Tang M, Zhou T, Do Y (2015) Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition. Sci Rep 5:9602CrossRefGoogle Scholar
  51. 51.
    Liu Y, Tang M, Zhou T, Do Y (2015) Improving the accuracy of the k-shell method by removing redundant links-from a perspective of spreading dynamics. Sci Rep 5:13172CrossRefADSGoogle Scholar
  52. 52.
    Lü L, Chen D, Ren XL, Zhang QM, Zhang YC, Zhou T (2016) Vital nodes identification in complex networks. Phys Rep 650:1–63MathSciNetCrossRefADSGoogle Scholar
  53. 53.
    Lü L, Zhang YC, Yeung CH, Zhou T (2011) Leaders in social networks, the delicious case. PLoS One 6(6):e21202CrossRefADSGoogle Scholar
  54. 54.
    Lü L, Zhou T, Zhang QM, Stanley HE (2016) The h-index of a network node and its relation to degree and coreness. Nat Commun 7:10168CrossRefADSGoogle Scholar
  55. 55.
    Luo S, Morone F, Sarraute C, Makse HA (2017) Inferring personal financial status from social network location. Nat Commun 8:15227CrossRefADSGoogle Scholar
  56. 56.
    Martin T, Zhang X, Newman M (2014) Localization and centrality in networks. Phys Rev E 90(5):052808CrossRefADSGoogle Scholar
  57. 57.
    Mézard M, Parisi G (2003) The cavity method at zero temperature. J Stat Phys 111(1):1–34MathSciNetCrossRefzbMATHGoogle Scholar
  58. 58.
    Min B, Liljeros F, Makse HA (2015) Finding influential spreaders from human activity beyond network location. PLoS One 10(8):e0136831CrossRefGoogle Scholar
  59. 59.
    Min B, Morone F, Makse HA (2016) Searching for influencers in big-data complex networks. In: Bunde A, Caro J, Karger J, Vogl G (eds) Diffusive spreading in nature, technology and society. Springer, ChamGoogle Scholar
  60. 60.
    Mislove A, Marcon M, Gummadi KP, Druschel P, Bhattacharjee B: Measurement and analysis of online social networks. In: Proceedings of the 7th ACM SIGCOMM conference on internet measurement. Association for Computing Machinery, New York, pp 29–42Google Scholar
  61. 61.
    Morone F, Makse HA (2015) Influence maximization in complex networks through optimal percolation. Nature 524:65–68CrossRefADSGoogle Scholar
  62. 62.
    Morone F, Min B, Bo L, Mari R, Makse HA (2016) Collective influence algorithm to find influencers via optimal percolation in massively large social media. Sci Rep 6:30062CrossRefADSGoogle Scholar
  63. 63.
    Morone F, Roth K, Min B, Stanley HE, Makse HA (2017) A model of brain activation predicts the neural collective influence map of the human brain. Proc Natl Acad Sci U S A 114(15):3849–3854CrossRefGoogle Scholar
  64. 64.
    Muchnik L, Pei S, Parra LC, Reis SD, Andrade Jr, JS, Havlin S, Makse HA (2013) Origins of power-law degree distribution in the heterogeneity of human activity in social networks. Sci Rep 3:1783CrossRefADSGoogle Scholar
  65. 65.
    Mugisha S, Zhou HJ (2016) Identifying optimal targets of network attack by belief propagation. Phys Rev E 94(1):012305CrossRefADSGoogle Scholar
  66. 66.
    Nemhauser GL, Wolsey LA, Fisher ML (1978) An analysis of approximations for maximizing submodular set functions–I. Math Program 14(1):265–294MathSciNetCrossRefzbMATHGoogle Scholar
  67. 67.
    Newman ME (2002) Spread of epidemic disease on networks. Phys Rev E 66(1):016128MathSciNetCrossRefADSGoogle Scholar
  68. 68.
    Newman ME, Strogatz SH, Watts DJ (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E 64(2):026118CrossRefADSGoogle Scholar
  69. 69.
    Pastor-Satorras R, Vespignani A (2001) Epidemic spreading in scale-free networks. Phys Rev Lett 86(14):3200CrossRefADSGoogle Scholar
  70. 70.
    Pastor-Satorras R, Vespignani A (2002) Immunization of complex networks. Phys Rev E 65(3):036104CrossRefADSGoogle Scholar
  71. 71.
    Pei S, Makse HA (2013) Spreading dynamics in complex networks. J Stat Mech: Theory Exp 2013(12):P12002CrossRefGoogle Scholar
  72. 72.
    Pei S, Muchnik L, Andrade Jr JS, Zheng Z, Makse HA (2014) Searching for superspreaders of information in real-world social media. Sci Rep 4:5547CrossRefADSGoogle Scholar
  73. 73.
    Pei S, Muchnik L, Tang S, Zheng Z, Makse HA (2015) Exploring the complex pattern of information spreading in online blog communities. PLoS One 10(5):e0126894CrossRefGoogle Scholar
  74. 74.
    Pei S, Tang S, Zheng Z (2015) Detecting the influence of spreading in social networks with excitable sensor networks. PLoS One 10(5):e0124848CrossRefGoogle Scholar
  75. 75.
    Pei S, Teng X, Shaman J, Morone F, Makse HA (2017) Efficient collective influence maximization in threshold models of behavior cascading with first-order transitions. Sci Rep 7:45240CrossRefADSGoogle Scholar
  76. 76.
    Radicchi F, Castellano C (2016) Leveraging percolation theory to single out influential spreaders in networks. Phys Rev E 93(6):062314CrossRefADSGoogle Scholar
  77. 77.
    Ramos M, Shao J, Reis SD, Anteneodo C, Andrade Jr JS, Havlin S, Makse HA (2015) How does public opinion become extreme? Sci Rep 5:10032CrossRefADSGoogle Scholar
  78. 78.
    Reis SD, Hu Y, Babino A, Andrade Jr JS, Canals S, Sigman M, Makse HA (2014) Avoiding catastrophic failure in correlated networks of networks. Nat Phys 10(10):762–767CrossRefGoogle Scholar
  79. 79.
    Restrepo JG, Ott E, Hunt BR (2006) Characterizing the dynamical importance of network nodes and links. Phys Rev Lett 97(9):094102CrossRefADSGoogle Scholar
  80. 80.
    Richardson M, Domingos P (2002) Mining knowledge-sharing sites for viral marketing. In: Proceedings of the 8th ACM SIGKDD international conference on knowledge discovery and data mining. Association for Computing Machinery, New York, pp 61–70Google Scholar
  81. 81.
    Rogers EM (2010) Diffusion of innovations. Simon and Schuster, LondonGoogle Scholar
  82. 82.
    Roth K, Morone F, Min B, Makse HA (2017) Emergence of robustness in networks of networks. Phys Rev E 95(6):062308CrossRefADSGoogle Scholar
  83. 83.
    Rybski D, Buldyrev SV, Havlin S, Liljeros F, Makse HA (2012) Communication activity in a social network: relation between long-term correlations and inter-event clustering. Sci Rep 2:560CrossRefADSGoogle Scholar
  84. 84.
    Sabidussi G (1966) The centrality index of a graph. Psychometrika 31(4):581–603MathSciNetCrossRefzbMATHGoogle Scholar
  85. 85.
    Seidman SB (1983) Network structure and minimum degree. Soc Netw 5(3):269–287MathSciNetCrossRefGoogle Scholar
  86. 86.
    Stauffer D, Aharony A (1994) Introduction to percolation theory. CRC press, Boca RatonzbMATHGoogle Scholar
  87. 87.
    Tang S, Teng X, Pei S, Yan S, Zheng Z (2015) Identification of highly susceptible individuals in complex networks. Physica A 432:363–372CrossRefADSGoogle Scholar
  88. 88.
    Teng X, Yan S, Tang S, Pei S, Li W, Zheng Z (2014) Individual behavior and social wealth in the spatial public goods game. Physica A 402:141–149MathSciNetCrossRefADSzbMATHGoogle Scholar
  89. 89.
    Teng X, Pei S, Morone F, Makse HA (2016) Collective influence of multiple spreaders evaluated by tracing real information flow in large-scale social networks. Sci Rep 6:36043CrossRefADSGoogle Scholar
  90. 90.
    Viswanath B, Mislove A, Cha M, Gummadi KP (2009) On the evolution of user interaction in facebook. In: Proceedings of the 2nd ACM workshop on online social networks. Association for Computing Machinery, New York, pp 37–42CrossRefGoogle Scholar
  91. 91.
    Watts DJ (2002) A simple model of global cascades on random networks. Proc Natl Acad Sci U S A 99(9):5766–5771MathSciNetCrossRefADSzbMATHGoogle Scholar
  92. 92.
    Watts DJ, Dodds PS (2007) Influentials, networks, and public opinion formation. J Constr Res 34(4):441–458CrossRefGoogle Scholar
  93. 93.
    Yan S, Tang S, Pei S, Jiang S, Zheng Z (2014) Dynamical immunization strategy for seasonal epidemics. Phys Rev E 90(2):022808CrossRefADSGoogle Scholar
  94. 94.
    Yan S, Tang S, Fang W, Pei S, Zheng Z (2015) Global and local targeted immunization in networks with community structure. J Stat Mech: Theory Exp 2015(8):P08010MathSciNetCrossRefGoogle Scholar
  95. 95.
    Zeng A, Zhang CJ (2013) Ranking spreaders by decomposing complex networks. Phys Lett A 377(14):1031–1035CrossRefADSGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Environmental Health Sciences, Mailman School of Public HealthColumbia UniversityNew YorkUSA
  2. 2.Levich Institute and Physics DepartmentCity College of New YorkNew YorkUSA

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