Behavioral Pattern in Mobile Phone Networks Described by the Generalized Extreme Value Distribution at Individual Level

Abstract

There is increasing interest in studying human interactive behaviors using the large dataset of mobile phone networks, with the weighted social network as a helpful model. This paper focuses on the question of how the digital world might influence social relationships. There is an argument in previous researches between the three different possibilities: with extra volume brought by convenience of communication devices, will people tend to deepen their strong ties or broaden their weak ties or keep a ＂no change mode.＂ Our idea to address this problem is to investigate the distributions of per-node weight rather than all weights in the mobile phone network. Using CDRs data of 32,000 active mobile phone users, the empirical finding shows that the distributions of the logarithmic weights follow the generalized extreme value (GEV) distribution. The shape parameter of the GEV distribution reveals the existence of a typical strategy. The typical strategy could be regarded as an ＂intrinsic strategy＂ which indicates that the majority of people have strategies similar to the typical one, while the rest deviate far from it. An ＂asymptotic no change mode＂ is found by examining the relationship between the shape parameter and the social connectivity K. Therefore, the three possibilities of the aforementioned argument are in fact harmonious rather than exclusive.