An analysis of social networks based on tera-scale telecommunication datasets

Abstract

With the popularization of mobile phone usage, telecommunication networks have turned into a socially binding medium. Considering the traces of human communication held inside these networks, telecommunication networks are now able to provide a proxy for human social networks. To study degree characteristics and structural properties in large-scale social networks, we gathered a tera-scale dataset of call detail records that contains ≈ 5 × 10 7 nodes and ≈ 3.6 × 10 10 links for three GSM (mobile) networks, as well as ≈ 1.4 × 10 7 nodes and ≈ 1.9 × 10 9 links for one PSTN (fixed-line) network. In this paper, we first empirically evaluate some statistical models against the degree distribution of the country's call graph and determine that a Pareto log-normal distribution provides the best fit, despite claims in the literature that power-law distribution is the best model. We then question how network operator, size, density, and location affect degree distribution to understand the parameters governing it in social networks. Our empirical analysis indicates that changes in density, operator and location do not show a particular correlation with degree distribution; however, the average degree of social networks is proportional to the logarithm of network size. We also report on the structural properties of the communication network. These novel results are useful for managing and planning communication networks.