Measuring Propagation with Temporal Webs

  • Aaron BramsonEmail author
  • Kevin Hoefman
  • Milan van den Heuvel
  • Benjamin Vandermarliere
  • Koen Schoors
Part of the Theoretical Biology book series (THBIO)


We present a form of temporal network called a “temporal web” that connects nodes across time into a single temporally extended acyclic directed graph as a way to capture contingent behaviors. This representation is especially useful for uncovering and measuring social influence. We first present the general temporal web technique and then use it to analyze three empirical datasets: political relationships in the game EVE Online, interbank loans of the Russian banking system, and Twitter posts regarding the H1N1 vaccine. For each dataset we provide a detailed breakdown of the contingent behaviors using an approach we call temporal influence abduction. We then construct a temporal web for each one and describe the patterns of propagation found. Based on these patterns of propagation we infer more general properties of influence and the impact of certain types of behaviors in each system.


  1. 1.
    Abell, P.: Structural balance in dynamic structures. Sociology 2(3), 333–352 (1968)CrossRefGoogle Scholar
  2. 2.
    Antal, T., Krapivsky, P.L., Redner, S.: Social balance on networks: the dynamics of friendship and enmity. Phys. D Nonlinear Phenom. 224(1), 130–136 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Axelrod, R., Bennett, D.S.: Landscape theory of aggregation. Br. J. Polit. Sci. 23(02), 211–233 (1993)CrossRefGoogle Scholar
  4. 4.
    Berger, J., Milkman, K.L.: What makes online content viral? J. Mark. Res. 49(2), 192–205 (2012)CrossRefGoogle Scholar
  5. 5.
    Bermingham, A., Smeaton, A.F.: On using Twitter to monitor political sentiment and predict election results. In: Sentiment Analysis Where AI Meets Psychology (SAAIP) Workshop at the International Joint Conference for Natural Language Processing (IJCNLP), Chiang Mai (2011)Google Scholar
  6. 6.
    Bollen, J., Mao, H., Zeng, X.: Twitter mood predicts the stock market. J. Comput. Sci. 2(1), 1–8 (2011)CrossRefGoogle Scholar
  7. 7.
    Braha, D., Bar-Yam, Y.: From centrality to temporary fame: dynamic centrality in complex networks. Complexity 12(2), 59–63 (2006)CrossRefGoogle Scholar
  8. 8.
    Bramson, A., Vandermarliere, B.: Dynamical properties of interaction data. J. Complex Netw. 4(1), 87–114 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bramson, A., Vandermarliere, B.: Benchmarking measures of network influence. Sci. Rep. 6, 34052 (2016)CrossRefGoogle Scholar
  10. 10.
    Buchanan, M.: Meltdown modelling. Nature (London) 460(7256), 680–682 (2009)CrossRefGoogle Scholar
  11. 11.
    Cartwright, D., Harary, F.: Structural balance: a generalization of Heider’s theory. Psychol. Rev. 63(5), 277–293 (1956)CrossRefGoogle Scholar
  12. 12.
    Chen, D., Lü, L., Shang, M.S., Zhang, Y.C., Zhou, T.: Identifying influential nodes in complex networks. Phys. A: Stat. Mech. Appl. 391(4), 1777–1787 (2012)CrossRefGoogle Scholar
  13. 13.
    Ciotti, V., Bianconi, G., Capocci, A., Colaiori, F., Panzarasa, P.: Degree correlations in signed social networks. Phys. A 422, 25–39 (2015)CrossRefGoogle Scholar
  14. 14.
    Colizza, V., Barrat, A., Barthelemy, M., Valleron, A.J., Vespignani, A.: Modeling the worldwide spread of pandemic influenza: baseline case and containment interventions. PLoS Med. 4(1), e13 (2007)CrossRefGoogle Scholar
  15. 15.
    Costantini, G., Perugini, M.: Generalization of clustering coefficients to signed correlation networks. PLoS ONE 9(2), e88669 (2014)CrossRefGoogle Scholar
  16. 16.
    Cui, J., Zhang, Y.Q., Li, X.: On the clustering coefficients of temporal networks and epidemic dynamics. In: 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013), pp. 2299–2302. IEEE, Beijing (2013)Google Scholar
  17. 17.
    Davis, J.A.: Clustering and structural balance in graphs. Hum. Relat. 20, 181–187 (1967)CrossRefGoogle Scholar
  18. 18.
    De Domenico, M., Lima, A., Mougel, P., Musolesi, M.: The anatomy of a scientific rumor. Sci. Rep. 3, 2980 (2013)CrossRefGoogle Scholar
  19. 19.
    Dekker, A.H.: Network centrality and super-spreaders in infectious disease epidemiology. In: 20th International Congress on Modelling and Simulation (MODSIM2013), Adelaide (2013)Google Scholar
  20. 20.
    Doreian, P., Mrvar, A.: Partitioning signed social networks. Soc. Netw. 31(1), 1–11 (2009)CrossRefzbMATHGoogle Scholar
  21. 21.
    DuBois, T., Golbeck, J., Srinivasan, A.: Predicting trust and distrust in social networks. In: 2011 IEEE Third International Conference on Privacy, Security, Risk and Trust (PASSAT) and 2011 IEEE Third International Conference on Social Computing (SocialCom), Boston, pp. 418–424 (2011)Google Scholar
  22. 22.
    Facchetti, G., Iacono, G., Altafini, C.: Computing global structural balance in large-scale signed social networks. PNAS 108(52), 20953–20958 (2011)CrossRefGoogle Scholar
  23. 23.
    Georg, C.P.: The effect of the interbank network structure on contagion and common shocks. J. Bank. Financ. 37(7), 2216–2228 (2013)CrossRefGoogle Scholar
  24. 24.
    Grindrod, P., Higham, D.J.: A matrix iteration for dynamic network summaries. SIAM Rev. 55(1), 118–128 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Guille, A., Favre, C.: Event detection, tracking, and visualization in Twitter: a mention-anomaly-based approach. Soc. Netw. Anal. Min. 5(1), 1–18 (2015)CrossRefGoogle Scholar
  26. 26.
    Haldane, A.: Rethinking the financial network. Speech delivered at the Financial Student Association, Amsterdam (2009)Google Scholar
  27. 27.
    Hansen, L.K., Arvidsson, A., Nielsen, F.A., Colleoni, E., Etter, M.: Good friends, bad news. Affect and virality in Twitter. In: Future Information Technology. Communications in Computer and Information Science, vol. 185, pp. 34–43. Springer, Berlin (2011)Google Scholar
  28. 28.
    Harary, F.: On the measurement of structural balance. Behav. Sci. 4(4), 306–323 (1959)MathSciNetGoogle Scholar
  29. 29.
    Heider, F.: Attitudes and cognitive organization. J. Psychol. 21, 107–122 (1946)CrossRefGoogle Scholar
  30. 30.
    Heimbach, I., Hinz, O.: The impact of content sentiment and emotionality on content virality. Int. J. Res. Mark. 33(3), 695–701 (2016)CrossRefGoogle Scholar
  31. 31.
    Holme, P.: Modern temporal network theory: a colloquium. Eur. Phys. J. B 88(9), 1–30 (2015)CrossRefGoogle Scholar
  32. 32.
    Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)CrossRefGoogle Scholar
  33. 33.
    Hummon, N.P., Doreian, P.: Some dynamics of social balance processes: bringing Heider back into balance theory. Soc. Netw. 25(1), 17–49 (2003)CrossRefGoogle Scholar
  34. 34.
    Hüser, A.C.: Too interconnected to fail: a survey of the interbank networks literature. Technical report. (2015)
  35. 35.
    Jahanbakhsh, K., Moon, Y.: The predictive power of social media: on the predictability of U.S. presidential elections using Twitter. In: arXiv preprint arXiv:1407.0622 (2014)Google Scholar
  36. 36.
    Karas, A., Schoors, K.: Heracles or sisyphus? Finding, cleaning and reconstructing a database of Russian banks. Working paper 327, Ugent (2005)Google Scholar
  37. 37.
    Karas, A., Schoors, K.: A guide to Russian banks data. SSRN. (2010)
  38. 38.
    Kempe, D., Kleinberg, J., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Automata, Languages and Programming, pp. 1127–1138. Springer, Berlin/Heidelberg (2005)Google Scholar
  39. 39.
    Kim, H., Anderson, R.: Temporal node centrality in complex networks. Phys. Rev. E 85(2), 026107 (2012)CrossRefGoogle Scholar
  40. 40.
    Kimura, M., Saito, K., Nakano, R., Motoda, H.: Extracting influential nodes on a social network for information diffusion. Data Min. Knowl. Discov. 20(1), 70–97 (2010)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Kitsak, M., Gallos, L.K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H.E., Makse, H.A.: Identification of influential spreaders in complex networks. Nat. Phys. 6, 888–893 (2010)CrossRefGoogle Scholar
  42. 42.
    Kumar, S., Liu, H., Mehta, S., Subramaniam, L.V.: From tweets to events: exploring a scalable solution for twitter streams. arXiv preprint arXiv:1405.1392 (2014)Google Scholar
  43. 43.
    Kwak, H., Lee, C., Park, H., Moon, S.: What is Twitter, a social network or a news media? In: Proceedings of the 19th International Conference on World Wide Web, pp. 591–600. ACM, Raleigh (2010)Google Scholar
  44. 44.
    Lampos, V.: On voting intentions inference from Twitter content: a case study on UK 2010 General Election. Computing Research Repository (CoRR). arXiv:1204.0423 (2012)Google Scholar
  45. 45.
    Lampos, V., De Bie, T., Cristianini, N.: Flu detector – tracking epidemics on twitter. In: ECML PKDD, Barcelona, pp. 599–602. Springer (2010)Google Scholar
  46. 46.
    Lampos, V., Lansdall-Welfare, T., Araya, R., Cristianini, N.: Analysing mood patterns in the United Kingdom through Twitter content. Computing Research Repository (CoRR). arXiv:1304.5507 (2013)Google Scholar
  47. 47.
    Lawyer, G.: Understanding the influence of all nodes in a network. Sci. Rep. 5, 8665 (2015)CrossRefGoogle Scholar
  48. 48.
    Lerman, K., Ghosh, R., Kang, J.H.: Centrality metric for dynamic networks. In: Proceedings of the Eighth Workshop on Mining and Learning with Graphs, Washington, DC, pp. 70–77. ACM (2010)Google Scholar
  49. 49.
    Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks and in social and media. In: CHI 2010: Machine Learning and Web Interactions, Atlanta, 10–15 Apr 2010 (2010)Google Scholar
  50. 50.
    Liu, B.: Sentiment Analysis: Mining Opinions, Sentiments, and Emotions. Cambridge University Press, New York (2015)CrossRefGoogle Scholar
  51. 51.
    Lü, L., Zhang, Y.C., Yeung, C.H., Zhou, T.: Leaders in social networks, the delicious case. PLoS ONE 6(6), e21202 (2011)CrossRefGoogle Scholar
  52. 52.
    Malliaros, F.D., Rossi, M.E.G., Vazirgiannis, M.: Locating influential nodes in complex networks. Sci. Rep. 6, 19307 (2016)CrossRefGoogle Scholar
  53. 53.
    Mantzaris, A.V., Higham, D.J.: Dynamic communicability predicts infectiousness. In: Temporal Networks, pp. 283–294. Springer, Heidelberg (2013)Google Scholar
  54. 54.
    Moro, E.: Temporal network of information diffusion in Twitter (2012). Google Scholar
  55. 55.
    Nicosia, V., Tang, J., Mascolo, C., Musolesi, M., Russo, G., Latora, V.: Graph metrics for temporal networks. In: Temporal Networks, pp. 15–40. Springer, Heidelberg (2013)Google Scholar
  56. 56.
    Pagolu, V.S., Challa, K.N.R., Panda, G., Majhi, B.: Sentiment analysis and of twitter and data for and predicting stock and market movements. In: International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), Sankt Goar (2016)Google Scholar
  57. 57.
    Pastor-Satorras, R., Vespignani, A.: Immunization of complex networks. Phys. Rev. E 65, 036104 (2002)CrossRefGoogle Scholar
  58. 58.
    Pfitzner, R., Scholtes, I., Garas, A., Tessone, C.J., Schweitzerk, F.: Betweenness preference: quantifying correlations in the topological dynamics of temporal networks. Phys. Rev. Lett. 110, 198701 (2013)CrossRefGoogle Scholar
  59. 59.
    Riquelme, F., González-Cantergiani, P.: Measuring user influence on Twitter: a survey. Inf. Process. Manag. 52(5), 949–975 (2016)CrossRefGoogle Scholar
  60. 60.
    Rocha, L.E., Blondel, V.D.: Flow motifs reveal limitations of the static framework to represent human interactions. Phys. Rev. E 87(4), 042814 (2013)CrossRefGoogle Scholar
  61. 61.
    Rocha, L.E., Masuda, N.: Random walk centrality for temporal networks. New J. Phys. 16(6), 063023 (2014)MathSciNetCrossRefGoogle Scholar
  62. 62.
    Saif, H., Fernández, M., He, Y., Alani, H.: Evaluation datasets for twitter sentiment analysis: a survey and a new dataset, the STS-Gold. In: 1st International Workshop on Emotion and Sentiment in Social and Expressive Media: Approaches and Perspectives from AI (ESSEM 2013), Turin (2013).
  63. 63.
    Salathé, M., Khandelwal, S.: Assessing vaccination sentiments with online social media: implications for infectious disease dynamics and control. PLoS Comput. Biol. 7(10), e1002199 (2011)CrossRefGoogle Scholar
  64. 64.
    Salathé, M., Vu, D.Q., Khandelwal, S., Hunter, D.R.: The dynamics of health behavior sentiments on a large online social network. EPJ Data Sci. 2(1), 1–12 (2013)CrossRefGoogle Scholar
  65. 65.
    Serrano, E., Iglesias, C.A.: Validating viral marketing strategies in Twitter via agent-based social simulation. Expert Syst. Appl. 50, 140–150 (2016)CrossRefGoogle Scholar
  66. 66.
    Sikic, M., Lancic A., Antulov-Fantulin, N., Stefancic, H.: Epidemic centrality – is there an underestimated epidemic impact of network peripheral nodes? Eur. Phys. J. B 86(10), 1–13 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  67. 67.
    Szell, M., Lambiotte, R., Thurner, S.: Multirelational organization of large-scale social networks in an online world. PNAS 107(31), 13636–13641 (2010)CrossRefGoogle Scholar
  68. 68.
    Taxidou, I., Fischer, P.M.: Online analysis of information diffusion in Twitter. In: Proceedings of the 23rd International Conference on World Wide Web, WWW’14 Companion, pp. 1313–1318. ACM, New York (2014)Google Scholar
  69. 69.
    Vandermarliere, B., Karas, A., Ryckebusch, J., Schoors, K.: Beyond the power law: uncovering stylized facts in interbank networks. Phys. A 428, 443–457 (2015)CrossRefGoogle Scholar
  70. 70.
    Viard, J., Latapy, M.: Identifying roles in an IP network with temporal and structural density. In: 2014 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), pp. 801–806. IEEE, New York (2014)Google Scholar
  71. 71.
    Wehmuth, K., Ziviani, A., Fleury, E.: A unifying model for representing time-varying graphs. In: 2015 IEEE International Conference on Data Science and Advanced Analytics (DSAA), pp. 1–10. IEEE (2015). doi:  10.1109/DSAA.2015.7344810
  72. 72.
    Xu, S., Wang, P.: Identifying important nodes by adaptive leaderrank. Phys. A 469, 654–664 (2017)CrossRefGoogle Scholar
  73. 73.
    Yu, Y., Berger-Wolf, T.Y., Saia, J., et al.: Finding spread blockers in dynamic networks. In: Advances in Social Network Mining and Analysis, pp. 55–76. Springer, Berlin/Heidelberg (2010)Google Scholar
  74. 74.
    Zhao, L., Cui, H., Qiu, X., Wang, X., Wang, J.: Sir rumor spreading model in the new media age. Phys. A 392(4), 995–1003 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Aaron Bramson
    • 1
    • 2
    • 3
    Email author
  • Kevin Hoefman
    • 2
  • Milan van den Heuvel
    • 4
  • Benjamin Vandermarliere
    • 4
  • Koen Schoors
    • 2
  1. 1.Laboratory for Symbolic Cognitive DevelopmentRiken Brain Science InstituteWakoJapan
  2. 2.Department of General EconomicsGhent UniversityGhentBelgium
  3. 3.Department of Software and Information SystemsUNC CharlotteCharlotteUSA
  4. 4.Departments of General Economics and PhysicsGhent UniversityGhentBelgium

Personalised recommendations