Advertisement

Utilizing the average node degree to assess the temporal growth rate of Twitter

  • Despoina Antonakaki
  • Sotiris Ioannidis
  • Paraskevi Fragopoulou
Original Article

Abstract

Several models have been proposed that describe the evolution of the graph properties of many online social networks (OSNs) and explain the behavior of their users. These models are essential for understanding the growth dynamics of the underlying social graph. One of the most prominent OSNs is Twitter, since it covers a significant part of the online worldwide population. Nevertheless, investigating the validity of these models on Twitter entails many difficulties. The size of Twitter and the limitations of its access API make extremely difficult the estimation of many graph properties and therefore the evaluation of the proposed models. In this study, we present a simple and efficient method to fit an already existing model, which describes the densification power law property of modern OSNs. This model states that the average degree of an OSN increases over time. In a case study, we assess this model in two large samples of Twitter, and we demonstrate how it can portray the altering growth periods of Twitter. Finally, we make some remarks on several events during the early period of Twitter that may have affected its growth rates.

Keywords

Twitter Evolution Average node degree Temporal growth rate Online social networks Densification power law 

Notes

Acknowledgements

We would like to thank the anonymous reviewers that provided valuable comments and feedback. We are also grateful to prof. Marian Boguna and Kolja Kleineberg for the discussions and the contribution on the infrastructure at the University of Barcelona. Also we would like to thank Hariton Efstathiades and Demetris Antoniades for their valuable comments as well as the University of Cyprus on the valuable contribution of their infrastructure in order to complete the experiments. This work was supported by the following research projects: FP7 Marie-Curie ITN iSocial funded by the EC under Grant Agreement No. 316808, UNICORN: Funded by the European Commission (H2020-ICT-2016-1/ICT-06-2016) and EUNITY: Funded by the European Commission (H2020-DS-2016-2017/DS-05-2016).

References

  1. Albert R, Jeong H, Barabási A-L (1999) Internet: diameter of the world-wide web, vol 401. Nature Publishing Group, London, pp 130–131Google Scholar
  2. Amaral LAN, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci 97(21):11,149–11,152CrossRefGoogle Scholar
  3. Backstrom L, Boldi P, Rosa M, Ugander J, Vigna S (2012) Four degrees of separation. In: Proceedings of the 3rd annual ACM web science conference on WebSci ’12, ACM Press, New York, NY, USA, pp 33–42. http://dl.acm.org/citation.cfm?id=2380718.2380723
  4. Barabási A (1999) Emergence of scaling in random networks. Science 286(5439):509–512.  https://doi.org/10.1126/science.286.5439.509 MathSciNetCrossRefzbMATHGoogle Scholar
  5. Barbieri N, Bonchi F, Manco G (2013) Cascade-based community detection. In: Proceedings of the sixth ACM international conference on web search and data mining, ACM, pp 33–42Google Scholar
  6. Barbieri N, Bonchi F, Manco G (2014) Who to follow and why: link prediction with explanations. In: Proceedings of the 20th ACM SIGKDD international conference on knowledge discovery and data mining, ACM, pp 1266–1275Google Scholar
  7. Batrinca B, Treleaven PC (2015) Social media analytics: a survey of techniques, tools and platforms. AI Soc 30(1):89–116CrossRefGoogle Scholar
  8. Benevenuto F, Magno G, Rodrigues T, Almeida V (2010) Detecting spammers on twitter. In: Annual collaboration, electronic messaging, anti-abuse and spam conference (CEAS)Google Scholar
  9. Bliss CA, Frank MR, Danforth CM, Dodds PS (2013) An evolutionary algorithm approach to link prediction in dynamic social networks. CoRR abs/1304.6257. http://dblp.uni-trier.de/db/journals/corr/corr1304.html#abs-1304-6257
  10. Bray P (2015) Social authority: our measure of Twitter influence. http://moz.com/blog/social-authority. Accessed 20 Aug 2017
  11. Broder A, Kumar R, Maghoul F, Raghavan P, Rajagopalan S, Stata R, Tomkins A, Wiener J (2000) Graph structure in the web. Comput Netw 33(1):309–320CrossRefGoogle Scholar
  12. Bryant M (2010) Twitter geo-fail? Only 0.23% of tweets geotagged. https://thenextweb.com/2010/01/15/twitter-geofail-023-tweets-geotagged/
  13. Chan J, Bailey J, Leckie C, Houle M (2012) ciForager: incrementally discovering regions of correlated change in evolving graphs. ACM Trans Knowl Discov Data 6(3):1–50.  https://doi.org/10.1145/2362383.2362385 CrossRefGoogle Scholar
  14. Chowdhury A (2010) State of Twitter spam. https://blog.twitter.com/2010/state-of-twitter-spam. Accessed 20 Aug 2017
  15. Duncan R (2007) Making the switch from Twitter to Jaiku. http://goo.gl/JMuhKA. Accessed 20 Aug 2017
  16. Gonçalves B, Perra N, Vespignani A (2011) Modeling users’ activity on twitter networks: validation of Dunbar’s number. PLoS ONE 6(8):e22,656.  https://doi.org/10.1371/journal.pone.0022656 CrossRefGoogle Scholar
  17. Grier C, Thomas K, Paxson V, Zhang M (2010) @ spam: the underground on 140 characters or less. In: Proceedings of the 17th ACM conference on Computer and communications security—CCS ’10, ACM Press, New York, NY, USA, p 27.  https://doi.org/10.1145/1866307.1866311
  18. Judge P (2010) Barracuda Labs 2010, annual security report. Techniical report. Barracuda Networks IncGoogle Scholar
  19. Kim E, Gilbert S, Edwards M, Graeff E (2009) Detecting sadness in 140 characters. Webecology projectGoogle Scholar
  20. Kleinberg J (2000) Navigation in a small world. Nature 406(6798):845.  https://doi.org/10.1038/35022643 CrossRefGoogle Scholar
  21. Kleineberg K-K, Boguñá M (2014) Evolution of the digital society reveals balance between viral and mass media influence. Phys Rev X 4(031):046.  https://doi.org/10.1103/PhysRevX.4.031046 Google Scholar
  22. Kleinberg JM, Kumar R, Raghavan P, Rajagopalan S, Tomkins AS (1999) The web as a graph: measurements, models, and methods. In: Asano T, Imai H, Lee DT, Nakano S, Tokuyama T (eds) Computing and combinatorics. Springer, Berlin, Heidelberg, pp 1–17Google Scholar
  23. Kumar R, Novak J, Tomkins A (2006) Structure and evolution of online social networks. In: Proceedings of the 12th ACM SIGKDD international conference on knowledge discovery and data mining—KDD ’06, ACM Press, New York, NY, USA, p 611.  https://doi.org/10.1145/1150402.1150476
  24. Kwak H, Lee C, Park H, Moon S (2010) What is Twitter, a social network or a news media? In: Proceedings of the 19th international conference on World wide web—WWW ’10, ACM Press, New York, NY, USA, p 591. http://dl.acm.org/citation.cfm?id=1772690.1772751
  25. Lardinois F (2008) Twitter survives Stevenote—but FriendFeed was the place to be. http://goo.gl/aGyGW0. Accessed 20 Aug 2017
  26. Leskovec J, Faloutsos C (2006) Sampling from large graphs. In: Proceedings of the 12th ACM SIGKDD international conference on knowledge discovery and data mining—KDD ’06, ACM Press, New York, NY, USA, p 631. http://dl.acm.org/citation.cfm?id=1150402.1150479
  27. Leskovec J, Kleinberg J, Faloutsos C (2005) Graphs over time: densification laws, shrinking diameters and possible explanations. In: Proceeding of the eleventh ACM SIGKDD international conference on knowledge discovery in data mining—KDD ’05, ACM Press, New York, NY, USA, p 177. http://dl.acm.org/citation.cfm?id=1081870.1081893
  28. Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans Knowl Discov Data: TKDD 1(1):2CrossRefGoogle Scholar
  29. Leskovec J, Backstrom L, Kumar R, Tomkins A (2008a) Microscopic evolution of social networks. In: Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining—KDD 08, ACM Press, New York, NY, USA, p 462.  https://doi.org/10.1145/1401890.1401948
  30. Leskovec J, Lang KJ, Dasgupta A, Mahoney MW (2008b) Statistical properties of community structure in large social and information networks. In: Proceeding of the 17th international conference on World Wide Web—WWW ’08, ACM Press, New York, NY, USA, p 695.  https://doi.org/10.1145/1367497.1367591
  31. Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11(2):431–441MathSciNetCrossRefzbMATHGoogle Scholar
  32. Meeder B, Karrer B, Sayedi A, Ravi R, Borgs C, Chayes J (2011) We know who you followed last summer: inferring social link creation times in twitter. In: Proceedings of the 20th international conference on World Wide Web, ACM, pp 517–526Google Scholar
  33. Morales A, Borondo J, Losada JC, Benito RM (2014) Efficiency of human activity on information spreading on twitter. Soc Netw 39:1–11CrossRefGoogle Scholar
  34. Myers SA, Sharma A, Gupta P, Lin J (2014) Information network or social network? The structure of the twitter follow graph. In: Proceedings of the companion publication of the 23rd international conference on World Wide Web companion, International World Wide Web Conferences Steering Committee, pp 493–498Google Scholar
  35. Newman ME (2005) Power laws, pareto distributions and Zipf’s law. Contemp Phys 46(5):323–351CrossRefGoogle Scholar
  36. Sadikov E, Martinez MMM (2009) Information propagation on twitter. CS322 project reportGoogle Scholar
  37. Shah D (2010) The March of Twitter: analysis of how and where Twitter spread. https://goo.gl/RiWs4n. Accessed 20 Aug 2017
  38. Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268CrossRefzbMATHGoogle Scholar
  39. Wei W, Carley KM (2015) Measuring temporal patterns in dynamic social networks. ACM Trans Knowl Discov Data 10(1):1–27.  https://doi.org/10.1145/2749465 CrossRefGoogle Scholar
  40. Widrich L (2011) How twitter evolved from 2006 to 2011. https://blog.bufferapp.com/how-twitter-evolved-from-2006-to-2011. Accessed 20 Aug 2017
  41. Wikipedia (2004) Timeline of twitter. https://en.wikipedia.org/wiki/Timeline_of_Twitter. Accessed 20 Aug 2017
  42. Yang J, Leskovec J (2011) Patterns of temporal variation in online media. In: Proceedings of the fourth ACM international conference on Web search and data mining, ACM, pp 177–186Google Scholar
  43. Ye S, Wu SF (2010) Measuring message propagation and social influence on twitter. com. SocInfo 10:216–231Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Despoina Antonakaki
    • 1
  • Sotiris Ioannidis
    • 1
  • Paraskevi Fragopoulou
    • 1
  1. 1.FORTH-ICSHeraklionGreece

Personalised recommendations