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Measuring Propagation with Temporal Webs

Part of the Theoretical Biology book series (THBIO)

Abstract

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.

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Notes

  1. 1.

    There is also no strict limitation that the interactions be instantaneous – they may be spans of time in which the agents are related – but that is a further extension beyond what we cover here. See [70, 71] for more information on link-stream graphs.

  2. 2.

    Originally it was formulated as an odd number of links across all paths, but the triad version has become dominant [1], cf. [22].

  3. 3.

    For our analysis below we distinguish among strongly and weakly balanced and frustrated. Thus for us being unbalanced implies being one of the two kinds of frustrated, but that is not the only terminology. ‘Balanced’ can also refer to what we call ‘strongly balanced’, and hence our ‘weakly balanced’ would be ‘unbalanced’ but not frustrated.

  4. 4.

    Triads can only share one or zero edges. If two triads share two edges, then they both also include the nodes that are the source and target of those edges. The minimum number of source and target nodes for two edges (in a non-reflexive and non-multigraph network) is three. If two triads share three nodes, then they are identical triads.

  5. 5.

    In future work we will compare these results to the subset of sovereign alliances. Because the standings of sovereign alliances have a larger effect on the players, we expect there to be a stricter adherence to structural balance, but here we are primarily interested in whether the temporal web approach can capture and detect frustration propagation.

  6. 6.

    A more nuanced approach involving continuous-time analyses of frustration dynamics also weights the edges by both the value set and considering both directions. Presenting such an analysis requires details into EVE and into structural balance considerations not pertinent to our goal here of demonstrating the use of temporal webs to track frustration propagation.

  7. 7.

    One can include all static focal node states, but the number of cases of triads staying non-existent overwhelms the effect of including the others so that the largest differences is one in ten thousand. Furthermore, a comparison of the existent static to the non-existent static cases shows that the neighbor transition proportions are similar to within one in a thousand, bolstering our claim that these static cases can act as a baseline.

  8. 8.

    In this chapter, we restrict ourselves to short-term loans, defined as loans with a maturity of less than a week. These account for more than 80% of the transactions both in terms of the number and of the volume. The reasons for this restriction is because the data provide information about the repayment date and not about the issuance date of the loans. This makes it hard to infer the exact duration of the connection between two banks for the long-term loans.

  9. 9.

    Because the loans we are using have a maturity of less than one week, it may not be the case that A still has an exposure to B in month t + 1 if the loan was initiated in t. However, we do not know the conditions of that repayment. The idea is that lending to a bank that is at risk of default does not immediately elevate the lender’s risk; failing to be paid back or having a high-risk asset on the books however may elevate a lender’s risk, and that shows up in the next balance sheet.

  10. 10.

    This includes retweets in both the old and the current form. The old form of retweet was just copy-pasting the other person’s text and manually adding RT. The current form of retweets was rolled out for everyone on Nov 19, 2009. The keywords included are: vaccine, vaccinated, vaccinate, vaccinating, immunized, immunize, immunization, and immunizing.

  11. 11.

    If both positivity and negativity have 5 tweets out of 10, then the sentiment ratio is 1:1. If they both have 5 out of 1000 then again the ratio is 1:1. However, in the former case they both have medium sentiment levels and in the later case they both have low sentiment levels. In other work we provide a combined sentiment measurement, but the added complication is beyond the scope of this work.

References

  1. Abell, P.: Structural balance in dynamic structures. Sociology 2(3), 333–352 (1968)

    CrossRef  Google Scholar 

  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)

    MathSciNet  CrossRef  MATH  Google Scholar 

  3. Axelrod, R., Bennett, D.S.: Landscape theory of aggregation. Br. J. Polit. Sci. 23(02), 211–233 (1993)

    CrossRef  Google Scholar 

  4. Berger, J., Milkman, K.L.: What makes online content viral? J. Mark. Res. 49(2), 192–205 (2012)

    CrossRef  Google Scholar 

  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. Bollen, J., Mao, H., Zeng, X.: Twitter mood predicts the stock market. J. Comput. Sci. 2(1), 1–8 (2011)

    CrossRef  Google Scholar 

  7. Braha, D., Bar-Yam, Y.: From centrality to temporary fame: dynamic centrality in complex networks. Complexity 12(2), 59–63 (2006)

    CrossRef  Google Scholar 

  8. Bramson, A., Vandermarliere, B.: Dynamical properties of interaction data. J. Complex Netw. 4(1), 87–114 (2015)

    MathSciNet  CrossRef  Google Scholar 

  9. Bramson, A., Vandermarliere, B.: Benchmarking measures of network influence. Sci. Rep. 6, 34052 (2016)

    CrossRef  Google Scholar 

  10. Buchanan, M.: Meltdown modelling. Nature (London) 460(7256), 680–682 (2009)

    CrossRef  Google Scholar 

  11. Cartwright, D., Harary, F.: Structural balance: a generalization of Heider’s theory. Psychol. Rev. 63(5), 277–293 (1956)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  13. Ciotti, V., Bianconi, G., Capocci, A., Colaiori, F., Panzarasa, P.: Degree correlations in signed social networks. Phys. A 422, 25–39 (2015)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  15. Costantini, G., Perugini, M.: Generalization of clustering coefficients to signed correlation networks. PLoS ONE 9(2), e88669 (2014)

    CrossRef  Google Scholar 

  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. Davis, J.A.: Clustering and structural balance in graphs. Hum. Relat. 20, 181–187 (1967)

    CrossRef  Google Scholar 

  18. De Domenico, M., Lima, A., Mougel, P., Musolesi, M.: The anatomy of a scientific rumor. Sci. Rep. 3, 2980 (2013)

    CrossRef  Google Scholar 

  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. Doreian, P., Mrvar, A.: Partitioning signed social networks. Soc. Netw. 31(1), 1–11 (2009)

    CrossRef  MATH  Google Scholar 

  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. Facchetti, G., Iacono, G., Altafini, C.: Computing global structural balance in large-scale signed social networks. PNAS 108(52), 20953–20958 (2011)

    CrossRef  Google Scholar 

  23. Georg, C.P.: The effect of the interbank network structure on contagion and common shocks. J. Bank. Financ. 37(7), 2216–2228 (2013)

    CrossRef  Google Scholar 

  24. Grindrod, P., Higham, D.J.: A matrix iteration for dynamic network summaries. SIAM Rev. 55(1), 118–128 (2013)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  26. Haldane, A.: Rethinking the financial network. Speech delivered at the Financial Student Association, Amsterdam (2009)

    Google Scholar 

  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. Harary, F.: On the measurement of structural balance. Behav. Sci. 4(4), 306–323 (1959)

    MathSciNet  Google Scholar 

  29. Heider, F.: Attitudes and cognitive organization. J. Psychol. 21, 107–122 (1946)

    CrossRef  Google Scholar 

  30. Heimbach, I., Hinz, O.: The impact of content sentiment and emotionality on content virality. Int. J. Res. Mark. 33(3), 695–701 (2016)

    CrossRef  Google Scholar 

  31. Holme, P.: Modern temporal network theory: a colloquium. Eur. Phys. J. B 88(9), 1–30 (2015)

    CrossRef  Google Scholar 

  32. Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  34. Hüser, A.C.: Too interconnected to fail: a survey of the interbank networks literature. Technical report. https://ssrn.com/abstract=2577241 (2015)

  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. Karas, A., Schoors, K.: Heracles or sisyphus? Finding, cleaning and reconstructing a database of Russian banks. Working paper 327, Ugent (2005)

    Google Scholar 

  37. Karas, A., Schoors, K.: A guide to Russian banks data. SSRN. http://ssrn.com/paper-1658468 (2010)

  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. Kim, H., Anderson, R.: Temporal node centrality in complex networks. Phys. Rev. E 85(2), 026107 (2012)

    CrossRef  Google Scholar 

  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)

    MathSciNet  CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. 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. 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. 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. 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. Lawyer, G.: Understanding the influence of all nodes in a network. Sci. Rep. 5, 8665 (2015)

    CrossRef  Google Scholar 

  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. 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. Liu, B.: Sentiment Analysis: Mining Opinions, Sentiments, and Emotions. Cambridge University Press, New York (2015)

    CrossRef  Google Scholar 

  51. Lü, L., Zhang, Y.C., Yeung, C.H., Zhou, T.: Leaders in social networks, the delicious case. PLoS ONE 6(6), e21202 (2011)

    CrossRef  Google Scholar 

  52. Malliaros, F.D., Rossi, M.E.G., Vazirgiannis, M.: Locating influential nodes in complex networks. Sci. Rep. 6, 19307 (2016)

    CrossRef  Google Scholar 

  53. Mantzaris, A.V., Higham, D.J.: Dynamic communicability predicts infectiousness. In: Temporal Networks, pp. 283–294. Springer, Heidelberg (2013)

    Google Scholar 

  54. Moro, E.: Temporal network of information diffusion in Twitter (2012). http://estebanmoro.org/2012/10/temporal-network-of-information-diffusion-in-twitter/

    Google Scholar 

  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. 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. Pastor-Satorras, R., Vespignani, A.: Immunization of complex networks. Phys. Rev. E 65, 036104 (2002)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  59. Riquelme, F., González-Cantergiani, P.: Measuring user influence on Twitter: a survey. Inf. Process. Manag. 52(5), 949–975 (2016)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  61. Rocha, L.E., Masuda, N.: Random walk centrality for temporal networks. New J. Phys. 16(6), 063023 (2014)

    MathSciNet  CrossRef  Google Scholar 

  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). http://oro.open.ac.uk/40660/

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  65. Serrano, E., Iglesias, C.A.: Validating viral marketing strategies in Twitter via agent-based social simulation. Expert Syst. Appl. 50, 140–150 (2016)

    CrossRef  Google Scholar 

  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)

    MathSciNet  CrossRef  MATH  Google Scholar 

  67. Szell, M., Lambiotte, R., Thurner, S.: Multirelational organization of large-scale social networks in an online world. PNAS 107(31), 13636–13641 (2010)

    CrossRef  Google Scholar 

  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. Vandermarliere, B., Karas, A., Ryckebusch, J., Schoors, K.: Beyond the power law: uncovering stylized facts in interbank networks. Phys. A 428, 443–457 (2015)

    CrossRef  Google Scholar 

  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. 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. Xu, S., Wang, P.: Identifying important nodes by adaptive leaderrank. Phys. A 469, 654–664 (2017)

    CrossRef  Google Scholar 

  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. 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)

    MathSciNet  CrossRef  Google Scholar 

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Bramson, A., Hoefman, K., van den Heuvel, M., Vandermarliere, B., Schoors, K. (2017). Measuring Propagation with Temporal Webs. In: Masuda, N., Holme, P. (eds) Temporal Network Epidemiology. Theoretical Biology. Springer, Singapore. https://doi.org/10.1007/978-981-10-5287-3_4

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