Temporal Networks pp 65-94

Part of the Understanding Complex Systems book series (UCS) | Cite as

Temporal Scale of Dynamic Networks

Chapter

Abstract

Interactions, either of molecules or people, are inherently dynamic, changing with time and context. Interactions have an inherent rhythm, often happening over a range of time scales. Temporal streams of interactions are commonly aggregated into dynamic networks for temporal analysis. Results of this analysis are greatly affected by the resolution at which the original data are aggregated. The mismatch between the inherent temporal scale of the underlying process and that at which the analysis is performed can obscure important insights and lead to wrong conclusions. In this chapter we describe the challenge of identifying the range of inherent temporal scales of a stream of interactions and of finding the dynamic network representation that matches those scales. We describe possible formalizations of the problem of identifying the inherent time scales of interactions and present some initial approaches at solving it, noting the advantages and limitations of these approaches. This is a nascent area of research and our goal is to highlight its importance and to establish a computational foundation for further investigations.

References

  1. 1.
    Ackerman, M., Ben-David, S., Loker, D.: Towards property-based classification of clustering paradigms. In: Lafferty, J., Williams, C.K.I., Shawe-Taylor, J., Zemel, R.S., Culotta, A. (eds.) Neural Information Processing Systems, pp. 10–18 (2010). http://nips.cc/
  2. 2.
    Baldock, K., Memmott, J., Ruiz-Guajardo, J., Roze, D., Stone, G.S.: Daily temporal structure in african savanna flower visitation networks and consequences for network sampling. Ecology 92, 687–698 (2011)CrossRefGoogle Scholar
  3. 3.
    Barabasi, A.L.: Bursts: The Hidden Pattern Behind Everything We Do. Dutton, New York (2010)Google Scholar
  4. 4.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Barron, A.R., Rissanen, J., Yu, B.: The minimum description length principle in coding and modeling. IEEE Trans. Inf. Theor. 44(6), 2743–2760 (1998)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Ben-David, S., Ackerman, M.: Measures of clustering quality: a working set of axioms for clustering. Neural Information Processing Systems, pp. 121–128 (2008)Google Scholar
  7. 7.
    Bender-deMoll, S., McFarland, D.A.: The art and science of dynamic network visualization. J. Soc. Struct. 7(2), 1206–1241 (2006)Google Scholar
  8. 8.
    Blonder, B., Wey, T.W., Dornhaus, A., James, R., Sih, A.: Temporal dynamics and network analysis. In: Methods in Ecology and Evolution, pp. 958–972. Blackwell Publishing Ltd., Oxford (2012)Google Scholar
  9. 9.
    Butts, C.T.: An axiomatic approach to network complexity. J. Math. Sociol. 24, 273–301 (2000)MATHCrossRefGoogle Scholar
  10. 10.
    Caceres, R.S., Berger-Wolf, T., Grossman, R.: Temporal scale of processes in dynamic networks. In: IEEE 11th ICDM Workshops, pp. 925–932 (2011)Google Scholar
  11. 11.
    Chapanond, A., Krishnamoorthy, M., Yener, B.: Graph theoretic and spectral analysis of enron email data. Comput. Math. Organ. Theor. 11, 265–281 (2005)MATHCrossRefGoogle Scholar
  12. 12.
    Chung, F., Lu, L., Vu, V.: Spectra of random graphs with given expected degrees. Proc. Natl. Acad. Sci. 100(11), 6313–6318 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Clauset, A., Eagle, N.: Persistence and periodicity in a dynamic proximity network. In: DIMACS Workshop on Computational Methods for Dynamic Interaction Networks. DIMACS, Piscataway (2007)Google Scholar
  14. 14.
    Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51(4), 661–703 (2009)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    Cross, P.C., Lloyd-Smith, J.O., Getz, W.M.: Disentangling association patterns in fission-fusion societies using african buffalo as an example. Anim. Behav. 69, 499–506 (2005)CrossRefGoogle Scholar
  16. 16.
    Eagle, N., Pentland, A.: Reality mining: sensing complex social systems. Pers. Ubiquitous Comput. V10(4), 255–268 (2006)CrossRefGoogle Scholar
  17. 17.
    Erdos, P., Renyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)MathSciNetGoogle Scholar
  18. 18.
    Feldmann, A., Gilbert, A.C., Willinger, W., Kurtz, T.: The changing nature of network traffic: scaling phenomena. Comput. Comm. Rev. 28, 5–29 (1998)CrossRefGoogle Scholar
  19. 19.
    Fischhoff, I.R., Sundaresan, S.R., Cordingley, J., Larkin, H.M., Sellier, M.J., Rubenstein, D.I.: Social relationships and reproductive state influence leadership roles in movements of plains zebra, equus burchellii. Anim. Behav. 73(5), 825–831 (2007). doi:10.1016/j.anbehav.2006.10.012CrossRefGoogle Scholar
  20. 20.
    Gao, Q., Li, M., Vitányi, P.M.B.: Applying MDL to learn best model granularity. Artif. Intell. 121(1–2), 1–29 (2000)MATHCrossRefGoogle Scholar
  21. 21.
    Hinde, R.A.: Interactions, relationships, and social structure. Man 11, 1–17 (1976)CrossRefGoogle Scholar
  22. 22.
    Holme, P.: Network reachability of real-world contact sequences. Phys. Rev. E 71, 046119 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012) ArXiv e-prints (2011)Google Scholar
  24. 24.
    Hu, B., Rakthanmanon, T., Hao, Y., Evans, S., Lonardi, S., Keogh, E.J.: Discovering the intrinsic cardinality and dimensionality of time series using mdl. In: ICDM, pp. 1086–1091. IEEE Computer Society, Washington (2011)Google Scholar
  25. 25.
    Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabasi, A.L.: The large-scale organization of metabolic networks. Nature 407(6804), 651–654 (2000)ADSCrossRefGoogle Scholar
  26. 26.
    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 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    Kempe, D., Kleinberg, J., Kumar, A.: Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci. 64(4), 820–842 (2002)MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Keogh, E.J., Chu, S., Hart, D., Pazzani, M.J.: An online algorithm for segmenting time series. In: ICDM, pp. 289–296. IEEE Computer Society, Washington (2001)Google Scholar
  29. 29.
    Kivelä, M., Pan, R.K., Kaski, K., Kertész, J., Saramäki, J., Karsai, M.: Multiscale analysis of spreading in a large communication network. J. Stat. Mech. Theor. Exp. 3, 5 (2012)Google Scholar
  30. 30.
    Kleinberg, J.: An impossibility theorem for clustering. In: Advances in Neural Information Processing Systems, pp. 446–453 (2002)Google Scholar
  31. 31.
    Kleinberg, J.: Bursty and hierarchical structure in streams. Data Min. Knowl. Discov. 7(4), 373–397 (2003)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Krings, G., Karsai, M., Bernharsson, S., Blondel, V.D., Saramäki, J.: Effects of time window size and placement on the structure of aggregated networks. CoRR abs/1202.1145 (2012). http://arxiv.org/abs/1202.1145 ArXiv e-prints (2012)
  33. 33.
    Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.: Trawling the web for emerging cyber-communities. Comput. Netw. 31(11–16), 1481–1493 (1999)CrossRefGoogle Scholar
  34. 34.
    Kumar, R., Novak, J., Tomkins, A.: Structure and evolution of online social networks. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 611–617. ACM, New York (2006)Google Scholar
  35. 35.
    Lahiri, M., Berger-Wolf, T.Y.: Structure prediction in temporal networks using frequent subgraphs. In: Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining, pp. 35–42. IEEE, New York (2007)Google Scholar
  36. 36.
    Lahiri, M., Maiya, A.S., Caceres, R.S., Habiba, Berger-Wolf, T.Y.: The impact of structural changes on predictions of diffusion in networks. In: Workshops Proceedings of the 8th IEEE International Conference on Data Mining, pp. 939–948. IEEE, New York (2008)Google Scholar
  37. 37.
    Meila, M.: Comparing clusterings: an axiomatic view. In: In ICML ’05: Proceedings of the 22nd international conference on Machine learning, pp. 577–584. ACM, New York (2005)Google Scholar
  38. 38.
    Miller, B.A., Bliss, N.T., Wolfe, P.J.: Toward signal processing theory for graphs and non-euclidean data. In: ICASSP, pp. 5414–5417. IEEE, New York (2010)Google Scholar
  39. 39.
    Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. Random Struct. Algorithms 6(2–3), 161–180 (1995)MathSciNetMATHCrossRefGoogle Scholar
  40. 40.
    Molloy, M., Reed, B.: The size of the giant component of a random graph with a given degree sequence. Comb. Probab. Comput. 7(3), 295–305 (1998)MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Moody, J., McFarland, D., Bender-deMoll, S.: Dynamic network visualization. Am. J. Sociol. 110(4), 1206–1241 (2005)CrossRefGoogle Scholar
  42. 42.
    Morris, M., Kretzschmar, M.: Concurrent partnerships and transmission dynamics in networks. Soc. Netw. 17, 299–318 (1995)CrossRefGoogle Scholar
  43. 43.
    Papadimitriou, S., Li, F., Kollios, G., Yu, P.S.: Time series compressibility and privacy. In: VLDB, pp. 459–470. VLDB Endowment, Vienna (2007)Google Scholar
  44. 44.
    Partridge, C., Cousins, D., Jackson, A.W., Krishnan, R., Saxena, T., Strayer, W.T.: Using signal processing to analyze wireless data traffic. In: Proceedings of the ACM Workshop on Wireless Security, pp. 67–76. ACM, New York (2002)Google Scholar
  45. 45.
    Pesaran, M.H., Timmermann, A.: Model instability and choice of observation window. Economics Working Paper Series 99–19, Department of Economics, UC San Diego, 1999Google Scholar
  46. 46.
    Riolo, C., Koopman, J., Chick, S.: Methods and measures for the description of epidemiologic contact networks. J. Urban Health 78, 446–457 (2001)CrossRefGoogle Scholar
  47. 47.
    Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)MATHCrossRefGoogle Scholar
  48. 48.
    Rubenstein, D., Sundaresan, S., Fischhoff, I., Saltz, D.: Social networks in wild asses: comparing patterns and processes among populations, pp. 159–176. Martin-Luther-University Halle-Wittenberg, Halle (2007)Google Scholar
  49. 49.
    Sedley, D.: The stoic criterion of identity. Phronesis 27, 255–75 (1982)CrossRefGoogle Scholar
  50. 50.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)MathSciNetGoogle Scholar
  51. 51.
    Shetty, J., Adibi, J.: Enron email dataset. Institute, USC Information Sciences (2004). http://www.isi.edu/adibi/Enron/Enron.htm
  52. 52.
    Silk, J., Alberts, S., Altmann, J.: Social relationships among adult female baboons ( < i > papio cynocephalus < /i > ) ii. variation in the quality and stability of social bonds. Behav. Ecol. Sociobiol. 61(2), 197–204 (2006)Google Scholar
  53. 53.
    Sulo, R., Berger-Wolf, T., Grossman, R.: Meaningful selection of temporal resolution for dynamic networks. In: Proceedings of the 8th Workshop on Mining and Learning with Graphs, MLG ’10, pp. 127–136. ACM, New York (2010)Google Scholar
  54. 54.
    Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: Graphscope: parameter-free mining of large time-evolving graphs. In: KDD ’07: Proceedings of the 13th ACM SIGKDD on Knowledge Discovery and Data Mining, pp. 687–696. ACM, New York (2007)Google Scholar
  55. 55.
    Sundaresan, S.R., Fischhoff, I.R., Dushoff, J., Rubenstein, D.I.: Network metrics reveal differences in social organization between two fission-fusion species, grevy’s zebra and onager. Oecologia, 140–149 (2006)Google Scholar
  56. 56.
    Tanaka, Y., Iwamoto, K., Uehara, K.: Discovery of time-series motif from multi-dimensional data based on mdl principle. Mach. Learn. 58(2–3), 269–300 (2005)MATHCrossRefGoogle Scholar
  57. 57.
    Tantipathananandh, C., Berger-Wolf, T., Kempe, D.: A framework for community identification in dynamic social networks. In: KDD ’07: Proceedings of the 13th ACM SIGKDD on Knowledge Discovery and Data Mining, pp. 717–726. ACM, New York (2007)Google Scholar
  58. 58.
    Yosef, N., Regev, A.: Impulse control: temporal dynamics in gene transcription. Cell 144, 886–896 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of Illinois at ChicagoChicagoUSA

Personalised recommendations