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Information Diffusion Backbone

From the Union of Shortest Paths to the Union of Fastest Path Trees
  • Huijuan WangEmail author
  • Xiu-Xiu Zhan
Chapter
Part of the Computational Social Sciences book series (CSS)

Abstract

Information diffusion on a network, either static or temporal (time evolving), has been modelled by e.g. shortest path routing and epidemic spreading processes. Information is assumed to diffuse along the shortest or fastest path/trajectory. Not all the links contribute to the information diffusion, namely, appear in a diffusion trajectory. For example, a link with a large weight in a static network seldom appears in the shortest path between any node pair. We address the question which kind of links are more likely to appear in a diffusion trajectory in two scenarios: information diffuses along the shortest path on a static weighted network and through the fastest path trees governed by the Susceptible-Infected epidemic spreading on a temporal network. We construct the information diffusion backbone to record the probability for each (static or temporal) link to appear in an information diffusion trajectory. Our theory and simulations show how network link weights influence the backbone. Our findings about links with what local topological properties contribute more to the actual information diffusion is crucial to tackle optimization problems such as which node pairs should be stimulated to link and at what time in order to maximize the speed or prevalence of information spreading.

Keywords

Information diffusion Temporal network Backbone Weighted network Shortest path Fastest path Betweenness 

References

  1. 1.
    Barabási, A.L.: Network Science. Cambridge University Press, Cambridge (2016)zbMATHGoogle Scholar
  2. 2.
    Braunstein, L., Wu, Z., Chen, Y., Buldyrev, S., Kalisky, T., Sreenivasan, S., Cohen, R., López, E., Havlin, S., Stanley, H.: Optimal path and minimal spanning trees in random weighted networks. I. J. Bifurcation and Chaos 17, 2215–2255 (2007). https://doi.org/10.1142/S0218127407018361 ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Chaintreau, A., Hui, P., Crowcroft, J., Diot, C., Gass, R., Scott, J.: Impact of human mobility on opportunistic forwarding algorithms. IEEE Trans. Mob. Comput. 6(6), 606–620 (2007)CrossRefGoogle Scholar
  4. 4.
    Chartrand, G., Lesniak, L.: Graphs and Digraphs. Chapman and Hall/CRC, London/Boca Raton (1996)zbMATHGoogle Scholar
  5. 5.
    Chartrand, G., Oellermann, O.R.: Applied and Algorithmic Graph Theory. Mcgraw-Hill College, New York City (1992)Google Scholar
  6. 6.
    Chen, Y., López, E., Havlin, S., Stanley, H.E.: Universal behavior of optimal paths in weighted networks with general disorder. Phys. Rev. Lett. 96, 068,702 (2006).  https://doi.org/10.1103/PhysRevLett.96.068702 CrossRefGoogle Scholar
  7. 7.
    Dnc emails network dataset – KONECT. http://konect.uni-koblenz.de/networks/dnc-temporalGraph
  8. 8.
    Eagle, N., (Sandy) Pentland, A.: Reality Mining: sensing complex social systems. Pers. Ubiquitous Comput. 10(4), 255–268 (2006)Google Scholar
  9. 9.
    Fournet, J., Barrat, A.: Contact patterns among high school students. PloS One 9(9), e107878 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    Génois, M., Vestergaard, C.L., Fournet, J., Panisson, A., Bonmarin, I., Barrat, A.: Data on face-to-face contacts in an office building suggest a low-cost vaccination strategy based on community linkers. Net. Sci. 3(3), 326–347 (2015)CrossRefGoogle Scholar
  11. 11.
    Goh, K.I., Oh, E., Jeong, H., Kahng, B., Kim, D.: Classification of scale-free networks. Proc. Natl. Acad. Sci. 99(20), 12,583–12,588 (2002).  https://doi.org/10.1073/pnas.202301299 MathSciNetCrossRefGoogle Scholar
  12. 12.
    Grady, D., Thiemann, C., Brockmann, D.: Robust classification of salient links in complex networks. Nat. Commun. 3, 864 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  14. 14.
    Haggle network dataset – KONECT. http://konect.uni-koblenz.de/networks/contact
  15. 15.
    Holme, P.: Modern temporal network theory: a colloquium. Eur. Phys. J. B 88(9), 234 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Hypertext 2009 network dataset – KONECT. http://konect.uni-koblenz.de/networks/sociopatterns-hypertext
  18. 18.
    Isella, L., Stehlé, J., Barrat, A., Cattuto, C., Pinton, J.F., Van den Broeck, W.: What’s in a crowd? analysis of face-to-face behavioral networks. J. Theor. Biol. 271(1), 166–180 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Isella, L., Stehlé’, J., Barrat, A., Cattuto, C., Pinton, J.F., den Broeck, W.V.: What’s in a crowd? analysis of face-to-face behavioral networks. J. Theor. Biol. 271(1), 166–180 (2011)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: densification and shrinking diameters. ACM Trans. Knowl. Discov. Data 1(1), 2 (2007)CrossRefGoogle Scholar
  21. 21.
    Liu, C., Zhan, X.X., Zhang, Z.K., Sun, G.Q., Hui, P.M.: How events determine spreading patterns: information transmission via internal and external influences on social networks. New J. Phys. 17(11), 113,045 (2015)CrossRefGoogle Scholar
  22. 22.
    Manufacturing emails network dataset – KONECT. http://konect.uni-koblenz.de/networks/radoslaw_email
  23. 23.
    Mastrandrea, R., Fournet, J., Barrat, A.: Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys. PloS One 10(9), e0136,497 (2015)CrossRefGoogle Scholar
  24. 24.
    Michalski, R., Palus, S., Kazienko, P.: Matching organizational structure and social network extracted from email communication. In: Lecture Notes in Business Information Processing, vol. 87, pp. 197–206. Springer, Berlin (2011)CrossRefGoogle Scholar
  25. 25.
    Newman, M.E.: Scientific collaboration networks. ii. shortest paths, weighted networks, and centrality. Phys. Rev. E 64(1), 016,132 (2001)Google Scholar
  26. 26.
    Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64(2), 026,118 (2001)CrossRefGoogle Scholar
  27. 27.
    Panzarasa, P., Opsahl, T., Carley, K.M.: Patterns and dynamics of users’ behavior and interaction: network analysis of an online community. J. Assoc. Inf. Sci. Technol. 60(5), 911–932 (2009)CrossRefGoogle Scholar
  28. 28.
    Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87(3), 925 (2015)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87, 925–979 (2015)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Qu, B., Wang, H.: Sis epidemic spreading with correlated heterogeneous infection rates. Physica A: Stat. Mech. Appl. 472, 13–24 (2017)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Qu, B., Wang, H.: Sis epidemic spreading with heterogeneous infection rates. IEEE Trans. Netw. Sci. Eng. 4, 177–186 (2017)CrossRefGoogle Scholar
  32. 32.
    Reality mining network dataset – KONECT. http://konect.uni-koblenz.de/networks/mit
  33. 33.
    Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. NeuroImage 52(3), 1059–1069 (2010). Computational Models of the BrainCrossRefGoogle Scholar
  34. 34.
    Scholtes, I., Wider, N., Pfitzner, R., Garas, A., Tessone, C.J., Schweitzer, F.: Causality-driven slow-down and speed-up of diffusion in non-markovian temporal networks. Nat. Commun. 5, 5024 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    Shekhtman, L.M., Bagrow, J.P., Brockmann, D.: Robustness of skeletons and salient features in networks. J. Complex Networks 2(2), 110–120 (2014)CrossRefGoogle Scholar
  36. 36.
    Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Isella, L., Pinton, J.F., Quaggiotto, M., Van den Broeck, W., Régis, C., Lina, B., et al.: High-resolution measurements of face-to-face contact patterns in a primary school. PloS One 6(8), e23,176 (2011)CrossRefGoogle Scholar
  37. 37.
    Valdano, E., Ferreri, L., Poletto, C., Colizza, V.: Analytical computation of the epidemic threshold on temporal networks. Phys. Rev. X 5(2), 021,005 (2015)Google Scholar
  38. 38.
    Van Mieghem, P., Magdalena, S.M.: A phase transition in the link weight structure of networks. Phys. Rev. E 72, 056,138 (2005)CrossRefGoogle Scholar
  39. 39.
    Van Mieghem, P., Wang, H.: The observable part of a network. IEEE/ACM Trans. Networking 17(1), 93–105 (2009).  https://doi.org/10.1109/TNET.2008.925089 CrossRefGoogle Scholar
  40. 40.
    Wang, H., Hernandez, J.M., Van Mieghem, P.: Betweenness centrality in a weighted network. Phys. Rev. E 77, 046,105 (2008)CrossRefGoogle Scholar
  41. 41.
    Wang, H., Douw, L., Hernández, J.M., Reijneveld, J.C., Stam, C.J., Van Mieghem, P.: Effect of tumor resection on the characteristics of functional brain networks. Phys. Rev. E 82, 021,924 (2010)CrossRefGoogle Scholar
  42. 42.
    Wang, H., Li, Q., D’Agostino, G., Havlin, S., Stanley, H.E., Van Mieghem, P.: Effect of the interconnected network structure on the epidemic threshold. Phys. Rev. E 88, 022,801 (2013)CrossRefGoogle Scholar
  43. 43.
    Watts, D.J.: A simple model of global cascades on random networks. Proc. Natl. Acad. Sci. USA 99(9), 5766–5771 (2002)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Zhan, X.X., Hanjalic, A., Wang, H.: Information diffusion backbones in temporal networks. Sci. Rep. 9(1), 6798 (2019)ADSCrossRefGoogle Scholar
  45. 45.
    Zhang, Z.K., Liu, C., Zhan, X.X., Lu, X., Zhang, C.X., Zhang, Y.C.: Dynamics of information diffusion and its applications on complex networks. Phys. Rep. 651, 1–34 (2016)ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    Zhang, Y.Q., Li, X., Vasilakos, A.V.: Spectral analysis of epidemic thresholds of temporal networks. IEEE Trans. Cybern. (to be published).  https://doi.org/10.1109/TCYB.2017.2743003
  47. 47.
    Zhang, Q., Karsai, M., Vespignani, A.: Link transmission centrality in large-scale social networks. EPJ Data Sci. 7(1), 33 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Delft University of TechnologyDelftThe Netherlands

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