中文摘要：

手机通信数据详细记录了人们的通信行为,成为研究人们社会关系、行为模式的重要资源.通话号码个数、通话次数和时长是手机通信网络的基本属性.本文在复杂网络理论基础上,应用统计的方法研究了中国西部某城市三百余万手机用户不同节假日和工作日的四天通话数据在不同尺度下的号码度、通话度、时长度的分布以及平均号码度、平均通话度、平均时长度的特征.研究表明,所有尺度下,号码度、通话度、时长度均为幂律分布,幂指数随尺度、日期和指标的不同而不同,在[1.3,4]范围内波动.总体上,号码度幂指数大于通话度和时长度幂指数,入度幂指数大于出度幂指数；节假日幂指数大于相应指标的工作日幂指数,休息时段幂指数大于工作时段幂指数；与工作日相比,节假日的平均号码度和平均通话度较小,平均时长度较大.揭示了绝大多数用户每日只接打1个号码的电话,节假日期间接打电话的用户数、次数、时长减少,但平均通话时长增大的特征.

英文摘要：

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.