Analysis on degree characteristics of mobile call network

Mobile phone data record the people's communication behaviors in detail, and become an important resource for studying people's social relationships and behavior patterns. The call numbers, call volumes and call durations are the basic properties of the mobile phone data network. Based on the theory of complex networks and the statistic method, studied in this paper are the degree distribution and average values of the call numbers, call volumes, call durations, by using the mobile phone call data of different holidays and workdays and different scales of day and period, which are produced by the 3.3 million subscribers registered in a western city in China. Research shows that at all scales the number degrees, volume degrees and duration degrees are all of power-law distribution, and the power exponents are different depending on the scale, date and index, and fluctuate from 1.3 to 4. In general, the number degree exponent is greater than that of the volume degree and duration degree, and the exponents of three indexes of in-degree are greater than those exponents of out-degree; the exponents in holidays are greater than those of the workdays, and the exponents in working periods are greater than those of non-working periods. Compared with in workdays, in holidays the average number degree and volume degree are small, and the average duration degree is large. It reveals that most of the subscribers call only one number in a day or a period, and the call numbers, call volumes and call durations all decrease on holidays or working periods, however the average call duration increases meanwhile