Mobile Phone Social Networks: Beyond Power-Law and Lognormal Distributions

We analyze a massive social network gathered from a large mobile phone operator’s records, comprised of millions of users and tens of millions of calls. We examine the following questions: what is the distribution of phone calls per customer; total talk time per customer; and distinct partners per customer? We find that these distributions are skewed, and that they significantly deviate from what would be expected by conventional wisdom, namely power-law and lognormal distributions. Instead, we propose the use of the recently formulated DPLN (Double Pareto Log Normal) distribution, and find a good fit for all metrics of interest (number of phone calls, total talk time, etc). Furthermore, we describe a generative process based on “social wealth”, that naturally results in the DPLN distributions we observe. Finally, we study the evolution of the parameters of these distributions over time, and their significance in modeling and forecasting.