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.
Similar content being viewed by others
References
Albert R, Jeong H, Barabási A-L (1999) Internet: diameter of the world-wide web, vol 401. Nature Publishing Group, London, pp 130–131
Amaral LAN, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci 97(21):11,149–11,152
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
Barabási A (1999) Emergence of scaling in random networks. Science 286(5439):509–512. https://doi.org/10.1126/science.286.5439.509
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 33–42
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 1266–1275
Batrinca B, Treleaven PC (2015) Social media analytics: a survey of techniques, tools and platforms. AI Soc 30(1):89–116
Benevenuto F, Magno G, Rodrigues T, Almeida V (2010) Detecting spammers on twitter. In: Annual collaboration, electronic messaging, anti-abuse and spam conference (CEAS)
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
Bray P (2015) Social authority: our measure of Twitter influence. http://moz.com/blog/social-authority. Accessed 20 Aug 2017
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):309–320
Bryant M (2010) Twitter geo-fail? Only 0.23% of tweets geotagged. https://thenextweb.com/2010/01/15/twitter-geofail-023-tweets-geotagged/
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
Chowdhury A (2010) State of Twitter spam. https://blog.twitter.com/2010/state-of-twitter-spam. Accessed 20 Aug 2017
Duncan R (2007) Making the switch from Twitter to Jaiku. http://goo.gl/JMuhKA. Accessed 20 Aug 2017
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
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
Judge P (2010) Barracuda Labs 2010, annual security report. Techniical report. Barracuda Networks Inc
Kim E, Gilbert S, Edwards M, Graeff E (2009) Detecting sadness in 140 characters. Webecology project
Kleinberg J (2000) Navigation in a small world. Nature 406(6798):845. https://doi.org/10.1038/35022643
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
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 1–17
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
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
Lardinois F (2008) Twitter survives Stevenote—but FriendFeed was the place to be. http://goo.gl/aGyGW0. Accessed 20 Aug 2017
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
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
Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans Knowl Discov Data: TKDD 1(1):2
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
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
Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11(2):431–441
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 517–526
Morales A, Borondo J, Losada JC, Benito RM (2014) Efficiency of human activity on information spreading on twitter. Soc Netw 39:1–11
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 493–498
Newman ME (2005) Power laws, pareto distributions and Zipf’s law. Contemp Phys 46(5):323–351
Sadikov E, Martinez MMM (2009) Information propagation on twitter. CS322 project report
Shah D (2010) The March of Twitter: analysis of how and where Twitter spread. https://goo.gl/RiWs4n. Accessed 20 Aug 2017
Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268
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
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
Wikipedia (2004) Timeline of twitter. https://en.wikipedia.org/wiki/Timeline_of_Twitter. Accessed 20 Aug 2017
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 177–186
Ye S, Wu SF (2010) Measuring message propagation and social influence on twitter. com. SocInfo 10:216–231
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).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Antonakaki, D., Ioannidis, S. & Fragopoulou, P. Utilizing the average node degree to assess the temporal growth rate of Twitter. Soc. Netw. Anal. Min. 8, 12 (2018). https://doi.org/10.1007/s13278-018-0490-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13278-018-0490-5