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The Effects of Local and Global Link Creation Mechanisms on Contagion Processes Unfolding on Time-Varying Networks

  • Kaiyuan Sun
  • Enrico Ubaldi
  • Jie Zhang
  • Márton Karsai
  • Nicola PerraEmail author
Chapter
Part of the Computational Social Sciences book series (CSS)

Abstract

Social closeness and popularity are key ingredients that shape the emergence and evolution of social connections over time. Social closeness captures local reinforcement mechanisms which are behind the formation of strong ties and communities. Popularity, on the other hand, describes global link formation dynamics which drive, among other things, hubs, weak ties and bridges between groups. In this chapter, we characterize how these mechanisms affect spreading processes taking place on time-varying networks. We study contagion phenomena unfolding on a family of artificial temporal networks. In particular, we revise four different variations of activity-driven networks that capture (i) heterogeneity of activation patterns (ii) popularity (iii) the emergence of strong and weak ties (iv) community structure. By means of analytical and numerical analyses we uncover a rich and process dependent phenomenology where the interplay between spreading phenomena and link formation mechanisms might either speed up or slow down the spreading.

Keywords

Activity driven networks Epidemic modeling Dynamical processes on time-varying networks Time-varying networks models Popularity Social closeness 

References

  1. 1.
    Granovetter, M.: The strength of weak ties. Am. J. Sociol. 78,1360–1380 (1973)CrossRefGoogle Scholar
  2. 2.
    Granovetter, M.: Getting a Job: A Study of Contacts and Careers. University of Chicago Press, Chicago (1995)CrossRefGoogle Scholar
  3. 3.
    Onnela, J.-P., Saramaki, J., Hyvonen, J., Szabo, G., Lazer, D., Kaski, K., Kertesz, J., Barabasi, A.-L.: Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. U.S.A. 104, 7332 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    Saramäki, J., Leicht, E.A., Ĺpez, E., Roberts, S.G., Reed-Tsochas, F., Dunbar, R.I.: Persistence of social signatures in human communication. Proc. Natl. Acad. Sci. 111(3), 942–947 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    Bakshy, E., Rosenn, I., Marlow, C., Adamic, L.: The role of social networks in information diffusion. In: Proceedings of the 21st International Conference on World Wide Web, pp. 519–528 (2012)Google Scholar
  6. 6.
    Levin, D.Z., Cross, R.: The strength of weak ties you can trust: the mediating role of trust in effective knowledge transfer. Manag. Sci. 50(11), 1477–1490 (2004)CrossRefGoogle Scholar
  7. 7.
    Friedkin, N.: A test of structural features of granovetter’s strength of weak ties theory. Soc. Networks 2(4), 411–422 (1980)CrossRefGoogle Scholar
  8. 8.
    Brown, J.J., Reingen, P.H.: Social ties and word-of-mouth referral behavior. J. Consum. Res. 14(3), 350–362 (1987)CrossRefGoogle Scholar
  9. 9.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486, 75–174 (2010)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Karsai, M., Iñiguez, G., Kaski, K., Kertész, J.: Complex contagion process in spreading of online innovation. J. R. Soc. Interface 11(101), 20140694 (2014)CrossRefGoogle Scholar
  11. 11.
    Karsai, M., Kivelä, M., Pan, R.K., Kaski, K., Kertész, J., Barabási, A.L., Saramäki, J. Small but slow world: How network topology and burstiness slow down spreading. Phys. Rev. E 83(2), 025102 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Weng, L., Karsai, M., Perra, N., Menczer, F., Flammini, A.: Attention on weak ties in social and communication networks. In: Complex Spreading Phenomena in Social Systems, pp. 213–228. Springer, Berlin (2018)Google Scholar
  13. 13.
    Burt, R.S.: Structural holes: The Social Structure of Competition. Harvard University Press, Cambridge (2009)Google Scholar
  14. 14.
    Newman, M.E.J.: Networks. An Introduction. Oxford Univesity Press, Oxford (2010)zbMATHCrossRefGoogle Scholar
  15. 15.
    Barabási, A.-L., et al.: Network Science. Cambridge University Press, Cambridge (2016)zbMATHGoogle Scholar
  16. 16.
    Holme, P.: Modern temporal network theory: a colloquium. Eur. Phys. J. B 88(9), 1–30 (2015)CrossRefGoogle Scholar
  17. 17.
    Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Perra, N., Gonçalves, B., Pastor-Satorras, R., Vespignani, A.: Activity driven modeling of time-varying networks. Sci. Rep. 2, 469 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    Ribeiro, B., Perra, N., Baronchelli, A.: Quantifying the effect of temporal resolution on time-varying networks. Sci. Rep. 3, 3006 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    Karsai, M., Perra, N., Vespignani, A.: Time varying networks and the weakness of strong ties. Sci. Rep. 4, 4001 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Tomasello, M. V., Perra, N., Tessone, C. J., Karsai, M., Schweitzer, F.: The role of endogenous and exogenous mechanisms in the formation of R&D networks. Sci. Rep. 4, 5679 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    Ubaldi, E., Perra, N., Karsai, M., Vezzani, A., Burioni, R. Vespignani, A.: Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation. Sci. Rep. 6, 35724 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    Alessandretti, L., Sun, K., Baronchelli, A.,Perra, N.: Random walks on activity-driven networks with attractiveness. Phys. Rev. E 95(5), 052318 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    Ubaldi, E., Vezzani, A., Karsai, M., Perra, N., Burioni, R.: Burstiness and tie activation strategies in time-varying social networks. Sci. Rep. 7, 46225 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    Starnini, M., Pastor-Satorras, R.: Temporal percolation in activity driven networks. Phys. Rev. E 89, 032807 (2014)ADSCrossRefGoogle Scholar
  26. 26.
    Holt-Lunstad, J., Smith, T. B., Layton, J. B.: Social relationships and mortality risk: a meta-analytic review. PLoS Med. 7(7), e1000316 (2010)CrossRefGoogle Scholar
  27. 27.
    Dunbar, R.I.M.: The social brain hypothesis and its implications for social evolution. Ann. Hum. Biol. 36(5), 562–572 (2009)CrossRefGoogle Scholar
  28. 28.
    Miritello, G., Moro, E., Lara, R.: Dynamical strength of social ties in information spreading. Phys. Rev. E 83, 045102 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    Stiller, J., Dunbar, R.I.M.: Perspective-taking and memory capacity predict social network size. Soc. Networks 29(1), 93–104 (2007)CrossRefGoogle Scholar
  30. 30.
    Powell, J., Lewis, P.A., Roberts, N., García-Fiñana, M., Dunbar, R.I.M.: Orbital prefrontal cortex volume predicts social network size: an imaging study of individual differences in humans. Proc. R. Soc. Lond. B Biol. Sci. 279, 2157–2162 (2012)CrossRefGoogle Scholar
  31. 31.
    Gonçalves, B., Perra, N., Vespignani, A. Modeling users’ activity on twitter networks: validation of dunbar’s number. PloS one 6(8), e22656 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    Laurent, G., Saramäki, J., Karsai, M.: From calls to communities: a model for time-varying social networks. Eur. Phys. J. B 88(11), 1–10 (2015)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Nadini, M., Sun, K., Ubaldi, E., Starnini, M., Rizzo, A., Perra, N.: Epidemic spreading in modular time-varying networks. Sci. Rep. 8(1), 2352 (2018)ADSCrossRefGoogle Scholar
  34. 34.
    Keeling, M.J., Rohani, P.: Modeling Infectious Disease in Humans and Animals. Princeton University Press, Princeton (2008)zbMATHCrossRefGoogle Scholar
  35. 35.
    Barrat, A., Barthélemy, M., Vespignani, A.: Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge (2008)zbMATHCrossRefGoogle Scholar
  36. 36.
    Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87(3), 925 (2015)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Wang, Z., Bauch, C.T., Bhattacharyya, S., d’Onofrio, A., Manfredi, P., Perc, M., Perra, N., Salathé, M., Zhao, D.: Statistical physics of vaccination. Phys. Rep. 664, 1–113 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Boguña, M., Castellano, C., Pastor-Satorras, R.: Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks. Phys. Rev. Lett. 111, 068701 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    Rizzo, A., Frasca, M., Porfiri, M.: Effect of individual behavior on epidemic spreading in activity driven networks. Phys. Rev. E 90, 042801 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    Zino, L., Rizzo, A., Porfiri, M.: Continuous-time discrete-distribution theory for activity-driven networks. Phys. Rev. Lett. 117(22), 228302 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    Pozzana, I., Sun, K., Perra, N.: Epidemic spreading on activity-driven networks with attractiveness. Phys. Rev. E 96(4), 042310 (2017)ADSCrossRefGoogle Scholar
  42. 42.
    Valdano, E., Ferreri, L., Poletto, C., Colizza, V.: Analytical computation of the epidemic threshold on temporal networks. Phys. Rev. X 5(2), 021005 (2015)Google Scholar
  43. 43.
    Prakash, B.A., Tong, H., Valler, M., Faloutsos, M.: Virus propagation on time-varying networks: theory and immunization algorithms. Mach. Learn. Knowl. Discovery Databases Lect. Notes Comput. Sci. 6323, 99–114 (2010)Google Scholar
  44. 44.
    Tizzani, M., Lenti, S., Ubaldi, E., Vezzani, A., Castellano, C., Burioni, R.: Epidemic spreading and aging in temporal networks with memory. Phys. Rev. E 98(6), 062315 (2018)ADSCrossRefGoogle Scholar
  45. 45.
    Sun, K., Baronchelli, A., Perra, N.: Contrasting effects of strong ties on sir and sis processes in temporal networks. Eur. Phys. J. B 88(12), 1–8 (2015)MathSciNetGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kaiyuan Sun
    • 1
  • Enrico Ubaldi
    • 2
  • Jie Zhang
    • 3
  • Márton Karsai
    • 4
    • 5
  • Nicola Perra
    • 3
    Email author
  1. 1.MOBS Lab, Network Science InstituteNortheastern UniversityBostonUSA
  2. 2.Sony Computer Science LaboratoriesParisFrance
  3. 3.Networks and Urban Systems CentreUniversity of GreenwichLondonUK
  4. 4.Department of Network and Data ScienceCentral European UniversityBudapestHungary
  5. 5.Univ Lyon, ENS de Lyon, Inria, CNRSUniversité Claude Bernard Lyon 1, LIPLyonFrance

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