Skip to main content Accessibility help

The evolution of a mobile payment solution network

  • Kjersti Aas (a1) and Hanne Rognebakke (a1)


Vipps is a peer-to-peer mobile payment solution launched by Norway’s largest financial services group DNB. The Vipps transaction data may be viewed as a graph with users corresponding to the nodes, and the financial transactions between the users defining the edges. We have followed the evolution of this graph from May 2015 to September 2016. This is a unique data set, as information about transactions of individuals is usually not available for research. In this paper, we use an advanced statistical model where preferential attachment is combined with fitness. We show that the intrinsic quality of the nodes in the Vipps network plays an important part in the evolution of the network. This insight may, e.g., be used to identify influential nodes for viral marketing.


Corresponding author

*Corresponding author. Emails:,


Hide All
Barabasi, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286, 509512.
Barabasi, A.-L., Albert, R., & Jeong, H. (2000). Scale-free characteristics of random networks: The topology of the world-wide web. Physica A: Statistical Mechanics and Its Applications, 281, 6977.
Bianconi, G., & Barabˡsi, A. L. (2001). Competition and multiscaling in evolving networks. Europhysics Letters, 54, 436442.
Borgs, C., Chayes, J., Daskalakis, C., & Roch, S. (2007). First to market is not everything: An analysis of preferential attachment with fitness. In Proceedings of the thirty-ninth annual acm symposium on theory of computing. STOC ‘07 (pp. 135144). New York, NY, USA: ACM.
Caldarelli, G., Capocci, A., De Los Rios, P., & Muñoz, M. A. (2002). Scale-free networks from varying vertex intrinsic fitness. Physical Review Letters, 89, 258702-1258702-4.
Callaway, D. S., Hopcroft, J. E., Kleinberg, J. M., Newman, M. E. J., & Strogatz, S. H. (2001). Are randomly grown graphs really random? Physical Review E, 64, 041902.
Cole, S. R., Chu, H., & Greenland, S. (2014). Maximum likelihood, profile likelihood, and penalized likelihood: A primer. American Journal of Epidemiology, 179, 252260.
Dereich, S., & Mörters, P. (2009). Random networks with sublinear preferential attachment: degree evolutions. Electronic Journal of Probability, 14, 12221267.
Hunter, D., & Lange, K. (2000). Quantile regression via an MM algorithm. Journal of Computational Statistics and Data Analysis, 9, 6077.
Iñiguez, G., Ruan, Z., Kaski, K., Kertész, J., & Karsai, M. (2017). Service adoption spreading in online social networks. arXiv preprint, arXiv:1706.09777.
Kondor, D., Posfai, M., Csabai, I., & Vattay, G. (2014). Do the rich get richer? An empirical analysis of the bitcoin transaction network. PLOS ONE, 9, e86197.
Kong, J. S., Sarshar, N., & Roychowdhury, V. P. (2008). Experience versus talent shapes the structure of the web. Proceedings of the National Academy of Sciences, 105(37), 1372413729.
Krapivsky, P. L., Redner, S., & Leyvraz, F. (2000). Connectivity of growing random networks. Physics Review Letters, 85, 46294632.
Krapivsky, P. L., Rodgers, G. J., & Redner, S. (2001). Organization of growing networks. Physical Review E, 63, 066123-1066123-14.
Kunegis, J., Blattner, M., & Moser, C. (2013). Preferential Attachment in Online Networks: Measurement and Explanations. Presented at WebSci’13 Conference, Paris.
Leskovec, J., Singh, A., & Kleinberg, J. (2006). Patterns of influence in a recommendation network. In Proceedings of the 10th pacific-asia conference on advances in knowledge discovery and data mining. PAKDD’06 (pp. 380389). Berlin, Heidelberg: Springer-Verlag.
Pham, T., Sheridan, P., & Shimodaira, H. (2015). PAFit: A statistical method for measuring preferential attachment in temporal complex networks. PLOS ONE, 9 , e0137796.
Pham, T., Sheridan, P., & Shimodaira, H. (2016). Joint estimation of preferential attachment and node fitness in the evolution of complex networks. Nature Scientific Reports, 6, 113.
Pham, T., Sheridan, P., & Shimodaira, H. (2017). PAFit: An R Package for Estimating Preferential Attachment and Node Fitness in Temporal Complex Networks. arXiv preprint, arXiv:1704.06017.
Redner, S. (1998). How popular is your paper? an empirical study of the citation distribution. The European Physical Journal B - Condensed Matter and Complex Systems, 4, 131134.
Stonedahl, F., Rand, W., & Wilensky, U. (2010). Evolving Viral Marketing Strategies. In Proceedings of the 12th annual conference on Genetic and evolutionary computation.
Yule, G. U. (1925). A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S. Philosophical Transactions of the Royal Society B, 213, 2187.


The evolution of a mobile payment solution network

  • Kjersti Aas (a1) and Hanne Rognebakke (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed