Skip to main content

A Map of Approaches to Temporal Networks

  • Chapter
  • First Online:
Temporal Network Theory

Abstract

The study of temporal networks is motivated by the simple and important observation that just as network structure can affect dynamics, so can structure in time, and just as network topology can teach us about the system in question, so can its temporal characteristics. In many cases, leaving out either one of these components would lead to an incomplete understanding of the system or poor predictions. Including time into network modeling, we argue, inevitably leads researchers away from the trodden paths of network science. Temporal network theory requires something different—new methods, new concepts, new questions—compared to static networks. In this introductory chapter, we give an overview of the ideas that the field of temporal networks has brought forward in the last decade. We also place the contributions to the current volume on this map of temporal-network approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ahmed, N.M., Chen, L.: An efficient algorithm for link prediction in temporal uncertain social networks. Inf. Sci. 331, 120–136 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  2. Arita, I., Nakane, M., Kojima, K., Yoshihara, N., Nakano, T., El-Gohary, A.: Role of a sentinel surveillance system in the context of global surveillance of infectious diseases. Lancet Infect. Dis. 4(3), 171–177 (2004)

    Article  Google Scholar 

  3. Backlund, V.P., Saramäki, J., Pan, R.K.: Effects of temporal correlations on cascades: threshold models on temporal networks. Phys. Rev. E 89, 062815 (2014)

    Article  ADS  Google Scholar 

  4. Bai, Y., Yang, B., Lin, L., Herrera, J.L., Du, Z., Holme, P.: Optimizing sentinel surveillance in temporal network epidemiology. Sci. Rep. 7(1), 4804 (2017)

    Article  ADS  Google Scholar 

  5. Barabási, A.-L.: The origin of bursts and heavy tails in human dynamics. Nature 435, 207–211 (2005)

    Article  ADS  Google Scholar 

  6. Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Barrat, A., Barthélemy, M., Pastor-Satorras, R., Vespignani, A.: The architecture of complex weighted networks. Proc. Natl. Acad. Sci. U.S.A. 101, 3747–3752 (2004)

    Article  ADS  Google Scholar 

  8. Barrat, A., Cattuto, C.: Temporal networks of face-to-face human interactions. In: P. Holme, J. Saramäki (eds.) Temporal Networks, pp. 191–216. Springer, Berlin (2013)

    Chapter  Google Scholar 

  9. Barthélemy, M., Barrat, A., Pastor-Satorras, R., Vespignani, A.: Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. Phys. Rev. Lett. 92, 178701 (2004)

    Article  ADS  Google Scholar 

  10. Batagelj, V., Doreian, P., Ferligoj, A., Kejzar, N.: Understanding Large Temporal Networks and Spatial Networks: Exploration, Pattern Searching, Visualization and Network Evolution. Wiley, London (2014)

    Google Scholar 

  11. Braunstein, A., Dall’Asta, L., Semerjian, G., Zdeborová, L.: Network dismantling. Proc. Natl. Acad. Sci. U.S.A. 113(44), 12368–12373 (2016)

    Article  Google Scholar 

  12. Britton, T.: Stochastic epidemic models: A survey. Math. Biosci. 225(1), 24–35 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Brudner, L.A., White, D.R.: Class, property, and structural endogamy: visualizing networked histories. Theory Soc. 26(2), 161–208 (1997)

    Article  Google Scholar 

  14. Cho, J.H., Gao, J.: Cyber war game in temporal networks. PLoS One 11(2), 1–16 (2016)

    Article  Google Scholar 

  15. Cho, Y.S., Galstyan, A., Brantingham, P.J., Tita, G.: Latent self-exciting point process model for spatial-temporal networks. Discrete Contin. Dynam. Syst. B 19(5), 1335–1354 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Colman, E.R., Vukadinović Greetham, D.: Memory and burstiness in dynamic networks. Phys. Rev. E 92, 012817 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  17. Danowski, J.A., Edison-Swift, P.: Crisis effects on intraorganizational computer-based communication. Commun. Res. 12(2), 251–270 (1985)

    Article  Google Scholar 

  18. Davis, A., Gardner, B.B., Gardner, M.R.: Deep South. The University of Chicago Press, Chicago (1941)

    Google Scholar 

  19. Delvenne, J.C., Lambiotte, R., Rocha, L.E.C.: Diffusion on networked systems is a question of time or structure. Nat. Commun. 6, 7366 (2015)

    Article  ADS  Google Scholar 

  20. Dinur, I., Safra, S.: On the hardness of approximating vertex cover. Ann. Math. 162(1), 439–485 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Enright, J., Kao, R.R.: Epidemics on dynamic networks. Epidemics 24, 88–97 (2018)

    Article  Google Scholar 

  22. Fefferman, N.H., Ng, K.L.: How disease models in static networks can fail to approximate disease in dynamic networks. Phys. Rev. E 76, 031919 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  23. Gauvin, L., Génois, M., Karsai, M., Kivelä, M., Takaguchi, T., Valdano, E., Vestergaard, C.L.: Randomized reference models for temporal networks (2018). arXiv:1806.04032

    Google Scholar 

  24. 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. Netw. Sci. 3(3), 326–347 (2015)

    Article  Google Scholar 

  25. Grönlund, A., Holme, P.: Networking the seceder model: group formation in social and economic systems. Phys. Rev. E 70, 036108 (2004)

    Article  ADS  Google Scholar 

  26. Gross, T., Sayama, H. (eds.): Adaptive Networks. Springer, Berlin (2009)

    MATH  Google Scholar 

  27. Gu, J., Lee, S., Saramäki, J., Holme, P.: Ranking influential spreaders is an ill-defined problem. Europhys. Lett. 118(6), 68002 (2017)

    Article  ADS  Google Scholar 

  28. Han, D., Sun, M., Li, D.: Epidemic process on activity-driven modular networks. Phys. A 432, 354–362 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  29. Hethcote, H.W.: The mathematics of infectious diseases. SIAM Rev. 42, 599 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Holme, P.: Network dynamics of ongoing social relationships. Europhys. Lett. 64, 427–433 (2003)

    Article  ADS  Google Scholar 

  31. Holme, P.: Network reachability of real-world contact sequences. Phys. Rev. E 71, 046119 (2005)

    Article  ADS  Google Scholar 

  32. Holme, P.: Epidemiologically optimal static networks from temporal network data. PLoS Comput. Biol. 9, e1003142 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  33. Holme, P.: Modern temporal network theory: a colloquium. Eur. Phys. J. B 88, 234 (2015)

    Article  ADS  Google Scholar 

  34. Holme, P., Liljeros, F.: Birth and death of links control disease spreading in empirical contact networks. Sci. Rep. 4, 4999 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. Hong, H., Ha, M., Park, H.: Finite-size scaling in complex networks. Phys. Rev. Lett. 98(25), 258701 (2007)

    Article  ADS  Google Scholar 

  37. Horváth, D.X., Kertész, J.: Spreading dynamics on networks: the role of burstiness, topology and non-stationarity. New J. Phys. 16(7), 073037 (2014)

    Article  ADS  Google Scholar 

  38. Huang, Q., Zhao, C., Zhang, X., Wang, X., Yi, D.: Centrality measures in temporal networks with time series analysis. Europhys. Lett. 118(3), 36001 (2017)

    Article  ADS  Google Scholar 

  39. Jo, H.H., Perotti, J.I., Kaski, K., Kertész, J.: Analytically solvable model of spreading dynamics with non-poissonian processes. Phys. Rev. X 4, 011041 (2014)

    Google Scholar 

  40. Johansen, A.: Probing human response times. Phys. A 330, 286–291 (2004)

    Article  Google Scholar 

  41. Karimi, F., Holme, P.: Threshold model of cascades in empirical temporal networks. Phys. A Stat. Mech. Appl. 392(16), 3476–3483 (2013)

    Article  Google Scholar 

  42. Karsai, M., Jo, H.H., Kaski, K. (eds.): Bursty Human Dynamics. Springer, Berlin (2018)

    Google Scholar 

  43. 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, 025102(R) (2011)

    Google Scholar 

  44. Karsai, M., Perra, N., Vespignani, A.: Time varying networks and the weakness of strong ties. Sci. Rep. 4, 4001 (2014)

    Article  ADS  Google Scholar 

  45. Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146. ACM, New York (2003)

    Google Scholar 

  46. Kim, B.J.: Geographical coarse graining of complex networks. Phys. Rev. Lett. 93, 168701 (2004)

    Article  ADS  Google Scholar 

  47. Kivelä, M., Cambe, J., Saramäki, J., Karsai, M.: Mapping temporal-network percolation to weighted, static event graphs. Sci. Rep. 8, 12357 (2018)

    Article  ADS  Google Scholar 

  48. Kivelä, M., Porter, M.A.: Estimating interevent time distributions from finite observation periods in communication networks. Phys. Rev. E 92, 052813 (2015)

    Article  ADS  Google Scholar 

  49. Krings, G., Karsai, M., Bernhardsson, S., Blondel, V.D., Saramäki, J.: Effects of time window size and placement on the structure of an aggregated communication network. EPJ Data Sci. 1(1), 4 (2012)

    Article  Google Scholar 

  50. Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21, 558–565 (1978)

    Article  MATH  Google Scholar 

  51. Lee, S.H., Holme, P.: Navigating temporal networks. Phys. A Stat. Mech. Appl. 513, 288–296 (2019)

    Article  Google Scholar 

  52. Lee, S.H., Kim, P.J., Jeong, H.: Statistical properties of sampled networks. Phys. Rev. E 73, 016102 (2006)

    Article  ADS  Google Scholar 

  53. Li, A., Cornelius, S.P., Liu, Y.Y., Wang, L., Barabási, A.L.: The fundamental advantages of temporal networks. Science 358, 1042–1046 (2017)

    Article  ADS  Google Scholar 

  54. Liben-Nowell, D., Kleinberg, J.: The link-prediction problem for social networks. J. Am. Soc. Inf. Sci. Technol. 58(7), 1019–1031 (2007)

    Article  Google Scholar 

  55. Liu, S., Perra, N., Karsai, M., Vespignani, A.: Controlling contagion processes in activity driven networks. Phys. Rev. Lett. 112, 118702 (2014)

    Article  ADS  Google Scholar 

  56. Liu, S.Y., Baronchelli, A., Perra, N.: Contagion dynamics in time-varying metapopulation networks. Phys. Rev. E 87, 032805 (2013)

    Article  ADS  Google Scholar 

  57. Masuda, N., Holme, P.: Predicting and controlling infectious disease epidemics using temporal networks. F1000Prime Rep. 5, 6 (2015)

    Google Scholar 

  58. Masuda, N., Lambiotte, R.: A Guide to Temporal Networks. World Scientific, Singapore (2016)

    Book  MATH  Google Scholar 

  59. Masuda, N., Rocha, L.E.C.: A Gillespie algorithm for non-markovian stochastic processes. SIAM Rev. 60, 95–115 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  60. Masuda, N., Takaguchi, T., Sato, N., Yano, K.: Self-exciting point process modeling of conversation event sequences. In: P. Holme, J. Saramäki (eds.) Temporal Networks, pp. 245–264. Springer, Berlin (2013)

    Chapter  Google Scholar 

  61. Mellor, A.: The temporal event graph. J. Complex Netw. 6, 639–659 (2018)

    Article  MathSciNet  Google Scholar 

  62. Min, B., Goh, K.I., Vazquez, A.: Spreading dynamics following bursty human activity patterns. Phys. Rev. E 83, 036102 (2011)

    Article  ADS  Google Scholar 

  63. Miritello, G., Moro, E., Lara, R.: Dynamical strength of social ties in information spreading. Phys. Rev. E 83, 045102 (2011)

    Article  ADS  Google Scholar 

  64. Morris, M., Kretzschmar, M.: Concurrent partnerships and transmission dynamics in networks. Soc. Netw. 17(3), 299–318 (1995). Social networks and infectious disease: HIV/AIDS

    Google Scholar 

  65. Mucha, P.J., Richardson, T., Macon, K., Porter, M.A., Onnela, J.P.: Community structure in time-dependent, multiscale, and multiplex networks. Science 328, 876–878 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  66. Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)

    Book  MATH  Google Scholar 

  67. Newman, M.E.J.: Estimating network structure from unreliable measurements. Phys. Rev. E 98(6), 062321 (2018)

    Article  ADS  Google Scholar 

  68. Onnela, J.P., Saramäki, J., Hyvönen, J., Szabó, G., Lazer, D., Kaski, K., Kertész, J., Barabási, A.L.: Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. 104, 7332–7336 (2007)

    Article  ADS  Google Scholar 

  69. Palla, G., Barabási, A.L., Vicsek, T.: Quantifying social group evolution. Nature 446, 664–667 (2007)

    Article  ADS  Google Scholar 

  70. Pan, R.K., Saramäki, J.: Path lengths, correlations, and centrality in temporal networks. Phys. Rev. E 84, 016105 (2011)

    Article  ADS  Google Scholar 

  71. Peel, L., Clauset, A.: Detecting change points in the large-scale structure of evolving networks. In: Twenty-Ninth AAAI Conference on Artificial Intelligence (2015)

    Google Scholar 

  72. Peixoto, T.P.: Network reconstruction and community detection from dynamics (2019). arXiv:1903.10833

    Google Scholar 

  73. Perra, N., Baronchelli, A., Mocanu, D., Gonçalves, B., Pastor-Satorras, R., Vespignani, A.: Random walks and search in time-varying networks. Phys. Rev. Lett. 109, 238701 (2012)

    Article  ADS  Google Scholar 

  74. Perra, N., Gonçalves, B., Pastor-Satorras, R., Vespignani, A.: Activity driven modeling of time varying networks. Sci. Rep. 4, 4001 (2014)

    Google Scholar 

  75. Rico-Gray, V., Díaz-Castelazo, C., Ramírez-Hernández, A., Guimarães, P.R., Holland, J.N.: Abiotic factors shape temporal variation in the structure of an ant–plant network. Arthropod Plant Interact. 6(2), 289–295 (2012)

    Article  Google Scholar 

  76. Rocha, L.E.C., Blondel, V.D.: Bursts of vertex activation and epidemics in evolving networks. PLoS Comput. Biol. 9(3), 1–9 (2013)

    Article  MathSciNet  Google Scholar 

  77. Rocha, L.E.C., Liljeros, F., Holme, P.: Simulated epidemics in an empirical spatiotemporal network of 50,185 sexual contacts. PLoS Comput. Biol. 7, 1–9 (2011)

    Article  Google Scholar 

  78. Rombach, M.P., Porter, M.A., Fowler, J.H., Mucha, P.J.: Core-periphery structure in networks. SIAM J. Appl. Math. 74(1), 167–190 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  79. Rossetti, G., Cazabet, R.: Community discovery in dynamic networks: a survey. ACM Comput. Surv. 51, 35 (2018)

    Article  Google Scholar 

  80. Rosvall, M., Bergstrom, C.T.: Mapping change in large networks. PLoS One 5(1), e8694 (2010)

    Article  ADS  Google Scholar 

  81. Rosvall, M., Esquivel, A.V., Lancichinetti, A., West, J.D., Lambiotte, R.: Memory in network flows and its effects on spreading dynamics and community detection. Nat. Commun. 5, 4630 (2014)

    Article  ADS  Google Scholar 

  82. Saramäki, J., Holme, P.: Exploring temporal networks with greedy walks. Eur. Phys. J. B 88(12), 334 (2015)

    Article  ADS  Google Scholar 

  83. Scellato, S., Leontiadis, I., Mascolo, C., Basu, P., Zafer, M.: Evaluating temporal robustness of mobile networks. IEEE Trans. Mob. Comput. 12(1), 105–117 (2013)

    Article  Google Scholar 

  84. Schaub, M.T., Delvenne, J.C., Rosvall, M., Lambiotte, R.: The many facets of community detection in complex networks. Appl. Netw. Sci. 2(1), 4 (2017)

    Article  Google Scholar 

  85. Sekara, V., Stopczynski, A., Lehmann, S.: Fundamental structures of dynamic social networks. Proc. Natl. Acad. Sci. U.S.A. 113(36), 9977–9982 (2016)

    Article  Google Scholar 

  86. Serrano, M.Á., Boguná, M., Vespignani, A.: Extracting the multiscale backbone of complex weighted networks. Proc. Natl. Acad. Sci. U.S.A. 106(16), 6483–6488 (2009)

    Article  ADS  Google Scholar 

  87. Sikdar, S., Ganguly, N., Mukherjee, A.: Time series analysis of temporal networks. Eur. Phys. J. B 89(1), 11 (2016)

    Article  ADS  Google Scholar 

  88. Song, C., Havlin, S., Makse, H.A.: Origins of fractality in the growth of complex networks. Nat. Phys. 2(4), 275 (2006)

    Article  Google Scholar 

  89. Starnini, M., Baronchelli, A., Barrat, A., Pastor-Satorras, R.: Random walks on temporal networks. Phys. Rev. E 85(5), 056115 (2012)

    Article  ADS  Google Scholar 

  90. Starnini, M., Baronchelli, A., Pastor-Satorras, R.: Modeling human dynamics of face-to-face interaction networks. Phys. Rev. Lett. 110, 168701 (2013)

    Article  ADS  Google Scholar 

  91. Starnini, M., Machens, A., Cattuto, C., Barrat, A., Pastor-Satorras, R.: Immunization strategies for epidemic processes in time-varying contact networks. J. Theor. Biol. 337, 89–100 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  92. Starnini, M., Pastor-Satorras, R.: Temporal percolation in activity-driven networks. Phys. Rev. E 89, 032807 (2014)

    Article  ADS  Google Scholar 

  93. Stopczynski, A., Sekara, V., Sapiezynski, P., Cuttone, A., Madsen, M.M., Larsen, J.E., Lehmann, S.: Measuring large-scale social networks with high resolution. PLoS One 9, e95978 (2014)

    Article  ADS  Google Scholar 

  94. 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), 326 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  95. Takaguchi, T., Masuda, N., Holme, P.: Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics. PLoS One 8, e68629 (2013)

    Article  ADS  Google Scholar 

  96. Takaguchi, T., Sato, N., Yano, K., Masuda, N.: Importance of individual events in temporal networks. New J. Phys. 14(9), 093003 (2012)

    Article  ADS  Google Scholar 

  97. Tang, J., Leontiadis, I., Scellato, S., Nicosia, V., Mascolo, C., Musolesi, M., Latora, V.: Applications of temporal graph metrics to real-world networks. In: P. Holme, J. Saramäki (eds.) Temporal Networks, pp. 135–159. Springer, Berlin (2013)

    Chapter  Google Scholar 

  98. Taylor, D., Myers, S.A., Clauset, A., Porter, M.A., Mucha, P.J.: Eigenvector-based centrality measures for temporal networks. Multiscale Model. Simul. 15(1), 537–574 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  99. Trajanovski, S., Scellato, S., Leontiadis, I.: Error and attack vulnerability of temporal networks. Phys. Rev. E 85, 066105 (2012)

    Article  ADS  Google Scholar 

  100. Ushio, M., Hsieh, C.H., Masuda, R., Deyle, E.R., Ye, H., Chang, C.W., Sugihara, G., Kondoh, M.: Fluctuating interaction network and time-varying stability of a natural fish community. Nature 554, 360–363 (2018)

    Article  ADS  Google Scholar 

  101. Vazquez, A., Rácz, B., Lukács, A., Barabási, A.L.: Impact of non-poissonian activity patterns on spreading processes. Phys. Rev. Lett. 98, 158702 (2007)

    Article  ADS  Google Scholar 

  102. Vestergaard, C.L., Génois, M., Barrat, A.: How memory generates heterogeneous dynamics in temporal networks. Phys. Rev. E 90, 042805 (2014)

    Article  ADS  Google Scholar 

  103. Zhan, X.X., Hanjalic, A., Wang, H.: Information diffusion backbones in temporal networks. Sci. Rep. 9, 6798 (2019)

    Article  ADS  Google Scholar 

  104. Zhang, Y., Wen, G., Chen, G., Wang, J., Xiong, M., Guan, J., Zhou, S.: Gaming temporal networks. IEEE Trans. Circuits Syst. Express Briefs 66(4), 672–676 (2019)

    Article  Google Scholar 

  105. Zhang, Y.Q., Li, X., Liang, D., Cui, J.: Characterizing bursts of aggregate pairs with individual poissonian activity and preferential mobility. IEEE Commun. Lett. 19(7), 1225–1228 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

PH was supported by JSPS KAKENHI Grant Number JP 18H01655. JS acknowledges support from the Academy of Finland, project “Digital Daily Rhythms” (project n:o 297195).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Petter Holme .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Holme, P., Saramäki, J. (2019). A Map of Approaches to Temporal Networks. In: Holme, P., Saramäki, J. (eds) Temporal Network Theory. Computational Social Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-23495-9_1

Download citation

Publish with us

Policies and ethics