Applications of Temporal Graph Metrics to Real-World Networks

  • John Tang
  • Ilias Leontiadis
  • Salvatore Scellato
  • Vincenzo Nicosia
  • Cecilia Mascolo
  • Mirco Musolesi
  • Vito Latora
Part of the Understanding Complex Systems book series (UCS)


Real world networks exhibit rich temporal information: friends are added and removed over time in online social networks; the seasons dictate the predator-prey relationship in food webs; and the propagation of a virus depends on the network of human contacts throughout the day. Recent studies have demonstrated that static network analysis is perhaps unsuitable in the study of real world network since static paths ignore time order, which, in turn, results in static shortest paths overestimating available links and underestimating their true corresponding lengths. Temporal extensions to centrality and efficiency metrics based on temporal shortest paths have also been proposed. Firstly, we analyse the roles of key individuals of a corporate network ranked according to temporal centrality within the context of a bankruptcy scandal; secondly, we present how such temporal metrics can be used to study the robustness of temporal networks in presence of random errors and intelligent attacks; thirdly, we study containment schemes for mobile phone malware which can spread via short range radio, similar to biological viruses; finally, we study how the temporal network structure of human interactions can be exploited to effectively immunise human populations. Through these applications we demonstrate that temporal metrics provide a more accurate and effective analysis of real-world networks compared to their static counterparts.


Betweenness Centrality Temporal Metrics Temporal Network Naive Method Containment Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was funded in part through EPSRC Project MOLTEN (EP/I017321/1) and the EU LASAGNE Project, Contract No.318132 (STREP).


  1. 1.
    Albert, R., Jeong, H., Barabási, A.-L.: Error and attack tolerance of complex networks. Nature 406(6794), 378–382 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    Barrat, A., Barthélemy, M., Vespignani, A.: Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge (2008)zbMATHCrossRefGoogle Scholar
  3. 3.
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Cabspotting Project. (2009). Accessed 27 Feb 2013
  5. 5.
    Callaway, D.S., Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Network robustness and fragility: percolation on random graphs. Phys. Rev. Lett. 85(25), 5468–5471 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    Cattuto, C., Van den Broeck, W., Barrat, A., Colizza, V., Pinton, J.-F., Vespignani, A.: Dynamics of person-to-person interactions from distributed RFID sensor networks. PLoS ONE 5(7), e11596 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    CBS News. Enron traders caught on tape. (2004). Accessed 27 February 2013
  8. 8.
    CBS News. Former Enron trader pleads guilty. (2004). Accessed 27 February 2013
  9. 9.
    Centola, D.: The spread of behavior in an online social network experiment. Science 329(5996), 1194–1197 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Chaintreau, A., Hui, P., Crowcroft, J., Diot, C., Gass, R., Scott, J.: Impact of human mobility on opportunistic forwarding algorithms. IEEE Trans. Mobile Comput. 6(6), 606–620 (2007)CrossRefGoogle Scholar
  11. 11.
    Chaintreau, A., Le Boudec, J.Y., Ristanovic, N.: The age of gossip: spatial mean field regime. In: Proceedings of SIGMETRICS ’09, pp. 109–120. ACM, New York (2009)Google Scholar
  12. 12.
    Christakis, N.A., Fowler, J.H.: The spread of obesity in a large social network over 32 years. N. Engl. J. Med. 357(4), 370–379 (2007)CrossRefGoogle Scholar
  13. 13.
    Christakis, N.A., Fowler, J.H.: The collective dynamics of smoking in a large social network. N. Engl. J. Med. 358(21), 2249–2258 (2008)CrossRefGoogle Scholar
  14. 14.
    Clauset, A., Eagle, N.: Persistence and periodicity in a dynamic proximity network. In: Proceedings of DIMACS Workshop on Computational Methods for Dynamic Interaction Networks, Rutgers University, Piscataway, 24–25 September 2007Google Scholar
  15. 15.
    Crucitti, P., Latora, V., Marchiori, M., Rapisarda, A.: Error and attack tolerance of complex networks. Physica A 340, 388–394 (2004)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Danon, L., House, T.A., Read, J.M., Keeling, M.J.: Social encounter networks: collective properties and disease transmission. J. R. Soc. Interface 9(76), 11 (2012)CrossRefGoogle Scholar
  17. 17.
    Eagle, N., Pentland, A.: Reality mining: sensing complex social systems. Pers. Ubiquit. Comput. 10(4), 255–268 (2006)CrossRefGoogle Scholar
  18. 18.
    Elkind, P., McLean, B.: The Smartest Guys in the Room: The Amazing Rise and Scandalous Fall of Enron. New York, Penguin (2004)Google Scholar
  19. 19.
    Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17–61 (1960)Google Scholar
  20. 20.
    Eubank, S., Guclu, H., Anil Kumar, V.S., Marathe, M.V., Srinivasan, A., Toroczkai, Z., Wang, N.: Modelling disease outbreaks in realistic urban social networks. Nature 429(6988), 180–184 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    Evans, C.H. Jr., Ildstad, S.T.: Small Clinical Trials: Issues and Challenges. National Academy of Sciences Press, Washington, DC (2001)Google Scholar
  22. 22.
    Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. In: Proceedings of SIGCOMM ’99, pp. 251–262. ACM, New York (1999)Google Scholar
  23. 23.
    Federal Energy Regulatory Commission. Addressing the 2000–2001 Western Energy Crisis. (2010). Accessed 27 Feb 2013
  24. 24.
    Funka, S., Gilada, E., Watkinsb, C., Jansena, V.A.A.: The spread of awareness and its impact on epidemic outbreaks. Proc. Natl. Acad. Sci. U.S.A. 106, 6872–6877 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    Gkantsidis, C., Karagiannis, T., Vojnovic, M.: Planet scale software updates. In: Proceedings of SIGCOMM ’06. ACM, New York (2006)Google Scholar
  26. 26.
    Holme, P., Kim, B.J., Yoon, C.N., Han, S.K.: Attack vulnerability of complex networks. Phys. Rev. E 65(5), 056109 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    Huberman, B.A., Adamic, L.A.: Growth dynamics of the world-wide web. Nature 401(6749), 131 (1999)ADSGoogle Scholar
  28. 28.
    Hypponen, M.: F-secure weblog: the grand opening! (2005). Accessed 27 Feb 2013
  29. 29.
    Keeling, M.J., Rohani, P.: Modeling Infectious Diseases in Human and Animals. Princeton University Press, Princeton (2007)Google Scholar
  30. 30.
    Kempe, D., Kleinberg, J., Kumar, A.: Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci 64(4), 820–842 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Kendall, M.G.: A new measure of rank correlation. Biometrika 30(1–2), 81–93 (1938)MathSciNetzbMATHGoogle Scholar
  32. 32.
    Kostakos, V.: Temporal graphs. Physica A 388(6), 1007–1023 (2009)MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    Leavitt, N.: Mobile phones: the next frontier for hackers? Computer 38(4), 20–23 (2005)CrossRefGoogle Scholar
  34. 34.
    Lee, S., Rocha, L.E.C., Liljeros, F., Holme, P.: Exploiting temporal network structures of human interaction to effectively immunize populations. PLoS ONE 7(5), e36439 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    Liljeros, F., Edling, C.R., Amaral, L.A.N.: Sexual networks: implications for the transmission of sexually transmitted infections. Microb. Infect. 5(2), 189–196 (2003)CrossRefGoogle Scholar
  36. 36.
    May, R.M.: Network structure and the biology of populations. Trends Ecol. Evol. 21(7), 394–399 (2006)CrossRefGoogle Scholar
  37. 37.
    Medina, A., Gursun, G., Basu, P., Matta, I.: On the universal generation of mobility models. In: Proceedings of IEEE/ACM MASCOTS ’10, Miami Beach, FL, August 2010Google Scholar
  38. 38.
    Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)zbMATHGoogle Scholar
  39. 39.
    Newman, M.E.J.: Mixing patterns in networks. Phys. Rev. E 67, 026126 (2003)MathSciNetADSCrossRefGoogle Scholar
  40. 40.
    Nicosia, V., Tang, J., Mascolo, C., Musolesi, M., Russo, G., Latora, V.: Graph metrics for temporal networks. In: Saramäki, J., Holme, P. (eds.) Temporal Networks. Springer, Berlin (2013)Google Scholar
  41. 41.
    Piorkowski, M., Sarafijanovic-Djukic, N., Grossglauser, M.: CRAWDAD data set epfl/mobility (v. 2009-02-24). Downloaded from (2009). Accessed 27 Feb 2013
  42. 42.
    Rachuri, K.K., Musolesi, M., Mascolo, C., Rentfrow, P.J., Longworth, C., Aucinas, A.: EmotionSense: a mobile phones based adaptive platform for experimental social psychology research. In: Proceedings of UbiComp ’10. ACM, New York (2010)Google Scholar
  43. 43.
    Salathé, M., Kazandjieva, M., Lee, J.W., Levis, P., Feldman, M.W., Jones, J.H.: A high-resolution human contact network for infectious disease transmission. In: Proceedings of the National Academy of Sciences of the USA, Washington, vol. 107, pp. 22020–22025, December 2010Google Scholar
  44. 44.
    Saramäki, J., Kaski, K.: Modelling development of epidemics with dynamic small-world networks. J. Theor. Biol. 234(3), 413–421 (2005)CrossRefGoogle Scholar
  45. 45.
    Scellato, S., Leontiadis, I., Mascolo, C., Basu, P., Zafer, M.: Evaluating temporal robustness of mobile networks. IEEE Trans. Mobile Comput. 12(1), 105–117 (2013). Google Scholar
  46. 46.
    Scott, J., Gass, R., Crowcroft, J., Hui, P., Diot, C., Chaintreau, A.: CRAWDAD data set cambridge/haggle (v. 2009-05-29). Downloaded from (2009). Accessed 27 Feb 2013
  47. 47.
    Shetty, J., Adibi, J.: Discovering important nodes through graph entropy the case of Enron email database. In: Proceedings of the 3rd International Workshop on Link Discovery, pp. 74–81. ACM, Chicago (2005)Google Scholar
  48. 48.
    Tang, J., Musolesi, M., Mascolo, C., Latora, V.: Temporal distance metrics for social network analysis. In: Proceedings of WOSN ’09, Barcelona, August 2009Google Scholar
  49. 49.
    Tang, J., Musolesi, M., Mascolo, C., Latora, V., Nicosia, V.: Analysing information flows and key mediators through temporal centrality metrics. In: Proceedings of ACM SNS ’10, Paris, April 2010Google Scholar
  50. 50.
    Tang, J., Mascolo, C., Musolesi, M., Latora, V.: Exploiting temporal complex network metrics in mobile malware containment. In: Proceedings of the 12th IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks (WOWMOM’11), Lucca, June 2011Google Scholar
  51. 51.
    Tang, J., Kim, H., Mascolo, C., Musolesi, M.: STOP: socio-temporal opportunistic patching of short range mobile malware. In: Proceedings of the 13th IEEE Symposium on a World of Wireless, Mobile and Multimedia Networks (WOWMOM’12), San Francisco, June 2012Google Scholar
  52. 52.
    Van Ruitenbeek, E., Courtney, T., Sanders, W.H., Stevens, F.: Quantifying the effectiveness of mobile phone virus response mechanisms. In: Proceedings of DNS ’07, 2007Google Scholar
  53. 53.
    Virus description: Bluetooth-worm:symos/cabir. (2004). Accessed 27 Feb 2013
  54. 54.
    Wang, P., Gonzalez, M.C., Hidalgo, C.A., Barabasi, A.-L.: Understanding the spreading patterns of mobile phone viruses. Science 324(5930), 1071–1076 (2009)ADSCrossRefGoogle Scholar
  55. 55.
    Washington Post. Enron fraud trial ends in 5 convictions. (2004). Accessed 27 Feb 2013
  56. 56.
    Wasserman, S., Faust, K.: Social Networks Analysis. Cambridge University Press, Cambridge (1994)Google Scholar
  57. 57.
    Zhu, Z., Cao, G., Zhu, S., Ranjan, S., Nucci, A.: A social network based patching scheme for worm containment in cellular networks. In: Proceedings of INFOCOM ’09, IEEE, Rio de Janeiro, April 2009Google Scholar
  58. 58.
    Zyba, G., Voelker, G.M., Liljenstam, M., Mehes, A., Johansson, P.: Defending mobile phones from proximity malware. In: Proceedings of INFOCOM ’09, IEEE, Rio de Janeiro, April 2009Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • John Tang
    • 1
  • Ilias Leontiadis
    • 1
  • Salvatore Scellato
    • 1
  • Vincenzo Nicosia
    • 1
    • 2
  • Cecilia Mascolo
    • 1
  • Mirco Musolesi
    • 3
  • Vito Latora
    • 2
    • 4
    • 5
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK
  2. 2.Laboratorio sui Sistemi ComplessiScuola Superiore di CataniaCataniaItaly
  3. 3.School of Computer ScienceUniversity of BirminghamBirminghamUK
  4. 4.School of Mathematical SciencesQueen Mary, University of LondonLondonUK
  5. 5.Dipartimento di Fisica e Astronomia and INFNUniversitá di Catania and INFNCataniaItaly

Personalised recommendations