手机通话网络度特征分析

余晓平; 裴韬

doi:10.7498/aps.62.208901

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.

关键词:

Abstract

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.

Keywords:

作者及机构信息

余晓平¹,
裴韬²

1.
新疆石河子大学信息科学与技术学院, 石河子 832003;

2.
中国科学院地理科学与资源研究所, 资源与环境信息系统国家重点实验室, 北京 100101

基金项目: 国家自然科学基金(批准号：41171345)和国家高技术研究发展计划 (批准号：2012AA12A403) 资助的课题．

Authors and contacts

Yu Xiao-Ping¹,
Pei Tao²

1.
College of Information Science and Technology, Shihezi University, Shihezi 832003, China;

2.
State Key Laboratory of Resources and Environmental Information System, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 41171345) and the National High Technology Research andDevelopment Program of China (Grant No. 2012AA12A403).

参考文献

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施引文献

[1]	Kwok R 2009 Nature 458 959
[2]	Barabási A L, Albert R 1999 Science 286 509
[3]	Yuan W G, Liu Y, Cheng J J, Xiong F 2013 Acta Phys. Sin. 62 038901 (in Chinese) [苑卫国, 刘云, 程军军, 熊菲 2013 62 038901]
[4]	Si X M, Liu Y 2011 Acta Phys. Sin. 60 078903 (in Chinese) [司夏萌, 刘云 2011 60 078903]
[5]	Chi L P, Wang R, Su H, Xu X P, Zhao J S, Li W, Cai X 2003 Chin. Phys. Lett. 20 1393
[6]	Aiello W, Chung F, Lu L Y 2000 Proceedings of 32nd Annual ACM Symposium on Theory of Computing Portland, OR, USA, May 21-23, 2000 p171
[7]	Onnela J P, Saramaki J, Hyvonen J, Szabo G, Lazer D, Kaski K, Kertesz J, Barabasi A L 2007 Proc. Nat. Acad. Sci. USA 104 7332
[8]	Lambiotte R, Blondel V D, de Kerchove C, Huens E, Prieur C, Smoreda Z, van Dooren P 2008 Physica A: Statist. Mech. Appl. 387 5317
[9]	Kang C G, Zhang Y, Ma X J, Liu Y 2013 Int. J. Geograph. Informa. Sci. 27 431
[10]	Zhang L, Liu Y 2008 Acta Phys. Sin. 57 5419 (in Chinese) [张立, 刘云 2008 57 5419]
[11]	Wu Y, Xiao J H, Wu Z Y, Yang J Z 2007 Acta Phys. Sin. 56 2037 (in Chinese) [吴晔, 肖井华, 吴智远, 杨俊忠 2007 56 2037]
[12]	Gong K, Tang M, Shang M S, Zhou T 2012 Acta Phys. Sin. 61 098901 (in Chinese) [龚凯, 唐明, 尚明生, 周涛 2012 61 098901]
[13]	Ai J, Zhao H, Carleyb K M, Su Z, Li H 2013 Chin. Phys. B 22 78902
[14]	Li M J, Wu Y, Liu W Q, Xiao J H 2009 Acta Phys. Sin. 58 5251 (in Chinese) [李明杰, 吴晔, 刘维清, 肖井华 2009 58 5251]
[15]	Wang H, Han J H, Deng L, Cheng K Q 2013 Acta Phys. Sin. 62 110505 (in Chinese) [王辉, 韩江洪, 邓林, 程克勤 2013 62 110505]
[16]	Xiong X, Hu Y 2012 Acta Phys. Sin. 61 150509 (in Chinese) [熊熙, 胡勇 2012 61 150509]
[17]	Zhang Y C, Liu Y, Zhang H F, Cheng H, Xiong F 2011 Acta Phys. Sin. 60 050501 (in Chinese) [张彦超, 刘云, 张海峰, 程辉, 熊菲 2011 60 050501]
[18]	Barabási A L 2005 Nature 435 207
[19]	Wang B H, Zhou T, Zhou C S 2012 J. Univ. Shanghai Sci. Technol. 34 103 (in Chinese) [汪秉宏, 周涛, 周昌松 2012 上海理工大学学报 34 103]
[20]	Hong W, Han X P, Zhou T, Wang B H 2009 Chin. Phys. Lett. 26 028902
[21]	Wu Y, Zhou C S, Xiao J H, Kurths J, Schellnhuber H J 2010 Proc. Nat. Acad. Sci. USA 107 18803
[22]	Zhao Z D, Xia H, Shang M S, Zhou T 2011 Chin. Phys. Lett. 28 068901
[23]	Jiang Z Q, Xie W J, Li M X, Podobnik B, Zhou W X, Stanley H E 2013 Proc. Nat. Acad. Sci. USA 110 1600
[24]	González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779
[25]	Song C, Qu Z, Blumm N, Barabási A L 2010 Science 327 1018
[26]	Li N N, Zhang N, Zhou T 2008 Comp. Syst. Comp. Sci. 5 43 (in Chinese) [李楠楠, 张宁, 周涛 2008 复杂系统与复杂性科学 5 43]
[27]	Dong Y W, Cai S M, Shang M S 2013 Acta Phys. Sin. 62 028901 (in Chinese) [董宇蔚, 蔡世民, 尚明生 2013 62 028901]
[28]	Zhao F, Liu J H, Zha Y L, Zhou T 2011 Acta Phys. Sin. 60 118902 (in Chinese) [赵飞, 刘金虎, 查一龙, 周涛 2011 60 118902]
[29]	Zhu J F, Han X P, Wang B H 2010 Chin. Phys. Lett. 27 68902
[30]	Ahas R, Aasa A, Silm S, Tiru M 2010 Transport. Res. C: Emerg. Technol. 18 45
[31]	Ahas R, Silm S, Järv O, Saluveer E, Tiru M 2010 J. Urban Technol. 17 3
[32]	Isaacman S, Becker R, Cáceres R, Kobourov S, Martonosi M, Rowland J, Varshavsky A 2011 Pervasive Computing. 9th International Conference, Pervasive San Francisco, CA, USA, June 2011 p133
[33]	Reades J, Calabrese F, Sevtsuk A, Ratti C 2007 IEEE Pervasive Computing 6 30
[34]	Calabrese F, Ratti C 2006 Networks and Communication Studies 20 247
[35]	Reades J, Calabrese F, Ratti C 2009 Environment and Planning B: Planning & Design 36 824
[36]	Pulselli R M, Romano P, Ratti C, Tiezzi E 2008 Int. J. Design Nature and Ecodynamics 3 121
[37]	Ratti C, Sevtsuk A, Huang S, Pailer R 2005 Proceedings of the 3rd Symposium on LBS & TeleCartography Vienna, Austria, November 28-30, 2005
[38]	Sun J B, Yuan J, Wang Y, Si H B, Shan X M 2011 Physica A: Statist. Mech. Appl. 390 929
[39]	Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501 (in Chinese) [徐赞新, 王钺, 司洪波, 冯振明 2011 60 040501]

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