Bursty egocentric network evolution in Skype


In this study we analyze the dynamics of the contact list evolution of millions of users of the Skype communication network. We find that egocentric networks evolve heterogeneously in time as events of edge additions and deletions of individuals are grouped in long bursty clusters, which are separated by long inactive periods. We classify users by their link creation dynamics and show that bursty peaks of contact additions are likely to appear shortly after user account creation. We also study possible relations between bursty contact addition activity and other user-initiated actions like free and paid service adoption events. We show that bursts of contact additions are associated with increases in activity and adoption—an observation that can inform the design of targeted marketing tactics.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. 1.

    There is also a possibility of “blocking” a user, but for the purposes of this research, contact blocking is treated as equivalent to contact deletion since the additional implications of blocking are irrelevant to the study.


  1. Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97 doi:10.1103/RevModPhys.74.47

    Article  MATH  Google Scholar 

  2. Backstrom L, Kumar R, Marlow C, Novak J, Tomkins A (2008) Preferential behavior in online groups. In: Proceedings of the international conference on web search and web data mining, WSDM '08. ACM, New York, pp 117–128 doi:10.1145/1341531.1341549

  3. Barabási AL (2005) The origin of bursts and heavy tails in human dynamics. Nature 435:207–211 doi:10.1038/nature03459

    Article  Google Scholar 

  4. Chaovalit P, Gangopadhyay A, Karabatis G, Chen Z (2011) Discrete wavelet transform-based time series analysis and mining. ACM Comput Surv 43(2):6:1–6:37 doi:10.1145/1883612.1883613

    Article  Google Scholar 

  5. Eckmann JP, Moses E, Sergi D (2004) Entropy of dialogues creates coherent structures in e-mail traffic. Proc Natl Acad Sci USA 101(40):14333–14337 doi:10.1073/pnas.0405728101

    MathSciNet  Article  MATH  Google Scholar 

  6. Fortunato S (2010) Community detection in graphs. Phys Rep 486(3-5):75–174 doi:10.1016/j.physrep.2009.11.002

    MathSciNet  Article  Google Scholar 

  7. Gaito S, Zignani M, Rossi GP, Sala A, Wang X, Zheng H, Zhao BY (2012) On the bursty evolution of online social networks. ACM (HotSocial'12) 1–8 doi:10.1145/2392622.2392623

  8. Goh KI, Barabási AL (2008) Burstiness and memory in complex systems. EPL (Europhys Lett) 81(1):48002 doi:10.1209/0295-5075/81/48002

    Article  Google Scholar 

  9. Gonçalves B, Perra N, Vespignani A (2011) Modeling users’ activity on twitter networks: validation of Dunbar’s number. PLoS One 6(8):e22656 doi:10.1371/journal.pone.0022656

    Article  Google Scholar 

  10. Hartigan JA, Wong MA (1979) A k-means clustering algorithm. JSTOR Appl Stat 28(1):100–108

    Article  MATH  Google Scholar 

  11. Holme P, Saramäki J (2012) Temporal networks. Phys Rep (in press) doi:10.1016/j.physrep.2012.03.001

  12. Jin Y, Lin C-Y, Matsuo Y, Ishizuka M (2012) Mining dynamic social networks from public news articles for company value prediction. Soc Netw Anal Min 2(3):217-228 doi:10.1007/s13278-011-0045-5

    Article  Google Scholar 

  13. Jo HH, Karsai M, Kertész J, Kaski K (2012) Circadian pattern and burstiness in mobile phone communication. New J Phys 14(1):013055 doi:10.1088/1367-2630/14/1/013055

    Article  Google Scholar 

  14. Karsai M, Kivelä M, Pan RK, Kaski K, Kertész J, Barabási AL, Saramäki J (2011) Small but slow world: how network topology and burstiness slow down spreading. Phys Rev E83(2):025102 doi:10.1103/PhysRevE.83.025102

    Article  Google Scholar 

  15. Karsai M, Kaski K, Barabási AL, Kertész J (2012a) Universal features of correlated bursty behaviour. Sci Rep 2:397 doi:10.1038/srep00397

    Article  Google Scholar 

  16. Karsai M, Kaski K, Kertész J (2012b) Correlated dynamics in egocentric communication networks. PLoS ONE 7(7):e40612. doi:10.1371/journal.pone.0040612

  17. Kivelä M, Pan RK, Kaski K, Kertész J, Saramäki J, Karsai M (2012) Multiscale analysis of spreading in a large communication network. J Stat Mech Theory Exp P03005 doi:10.1088/1742-5468/2012/03/P03005

  18. Ko Y-K, Lou J-K, Li C-T, Lin S-D, Jeng S-K (2012) A social network evolution model based on seniority. Soc Netw Anal Min 2(2):107-119 doi:10.1007/s13278-011-0036-6

    Article  Google Scholar 

  19. Kovanen L, Karsai M, Kaski K, Kertész J, Saramäki J (2011) Temporal motifs in time-dependent networks. J Stat Mech Theory Exp 2011(11):P11005 doi:10.1088/1742-5468/2011/11/P11005

    Article  Google Scholar 

  20. Krings G, Calabrese F, Ratti C, Blondel VD (2009) Urban gravity: a model for inter-city telecommunication flows. J Stat Mech Theory Exp 2009(07):L07003 doi:10.1088/1742-5468/2009/07/L07003

    Article  Google Scholar 

  21. Krings G, Karsai M, Bernharsson S, Blondel VD, Saramäki J (2012) Effects of time window size and placement on the structure of aggregated networks. EPJ Data Sci 1(1):4 doi:10.1140/epjds4

    Article  Google Scholar 

  22. Leskovec J, Backstrom L, Kumar R, Tomkins A (2008) Microscopic evolution of social networks. In: Proceedings of the 14th ACM SIGKDD international conference on knowledge discovery and data mining, KDD '08. ACM, New York, pp 462–470 doi:10.1145/1401890.1401948

  23. Lin J, Keogh E, Lonardi S, Chiu B (2003) A symbolic representation of time series, with implications for streaming algorithms. In: Proceedings of the 8th ACM SIGMOD workshop on research issues in data mining and knowledge discovery, DMKD '03. ACM, New York, pp 2–11 doi:10.1145/882082.882086

  24. Lin J, Keogh E, Wei L, Lonardi S (2007) Experiencing sax: a novel symbolic representation of time series. Data Min Knowl Discov 15(2):107–144 doi:10.1007/s10618-007-0064-z

    MathSciNet  Article  Google Scholar 

  25. Malmgren RD, Stouffer DB, Motter AE, Amaral LAN (2008) A poissonian explanation for heavy tails in e-mail communication. Proc Natl Acad Sci 105(47):18153–18158 doi:10.1073/pnas.0800332105

    Article  Google Scholar 

  26. Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298(5594):824–827 doi:10.1126/science.298.5594.824

    Article  Google Scholar 

  27. Miritello G, Moro E, Lara R (2011) Dynamical strength of social ties in information spreading. Phys Rev E 83(4):045102 doi:10.1103/PhysRevE.83.045102

    Article  Google Scholar 

  28. Onnela JP, Saramäki J, Hyvönen J, Szabó G, Lazer D, Kaski K, Kertész J, Barabási AL (2007) Structure and tie strengths in mobile communication networks. Proc Natl Acad Sci 104(18):7332–7336 doi:10.1073/pnas.0610245104

    Article  Google Scholar 

  29. Rybski D, Buldyrev SV, Havlin S, Liljeros F, Makse HA (2009) Scaling laws of human interaction activity. Proc Natl Acad Sci 106(31):12640–12645 doi:10.1073/pnas.0902667106

    Article  Google Scholar 

  30. Stehlé J, Barrat A, Bianconi G (2010) Dynamical and bursty interactions in social networks. Phys Rev E 81(3):1–5 doi:10.1103/PhysRevE.81.035101

    Article  Google Scholar 

Download references


The authors gratefully acknowledge the support of André Karpištšenko and Ando Saabas from Skype Technologies. This research was partly funded by the ERDF via the Software Technology and Applications Competence Centre (STACC) and Skype Technologies. M.K. thanks K. Kaski and J. Kertész for useful discussions and acknowledges support from FP7 ICTeCollective Project (No. 238597).

Author information



Corresponding author

Correspondence to Márton Karsai.

Electronic supplementary material

Below is the link to the electronic supplementary material.

PDF (114 KB)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kikas, R., Dumas, M. & Karsai, M. Bursty egocentric network evolution in Skype. Soc. Netw. Anal. Min. 3, 1393–1401 (2013). https://doi.org/10.1007/s13278-013-0123-y

Download citation


  • Data mining
  • Online social networks
  • Human dynamics
  • Social network evolution