Mobile Call Graphs-Beyond Power Law and Lognormal Distributions

We analyze a massive social network, gathered from the records of a large mobile phone operator, with more than a million users and tens of millions of calls. We examine the distributions of the number of phone calls per customer; the total talk minutes per customer; and the distinct number of calling partners per customer. We find that these distributions are skewed, and that they significantly deviate from what would be expected by power-law and lognormal distributions. To analyze our observed distributions (of number of calls, distinct call partners, and total talk time), we propose PowerTrack , a method which fits a lesser known but more suitable distribution, namely the Double Pareto LogNormal (DPLN) distribution, to our data and track its parameters over time. Using PowerTrack , we find that our graph changes over time in a way consistent with a generative process that naturally results in the DPLN distributions we observe. Furthermore, we show that this generative process lends itself to a natural and appealing social wealth interpretation in the context of social networks such as ours. We discuss the application of those results to our model and to forecasting.

Free download research paper

COMMENT free research papers, wireless