Analysis on degree characteristics of mobile call network

Yu Xiao-Ping; Pei Tao

doi:10.7498/aps.62.208901

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:

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).

References

[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]

Cited By

[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]

[1]	Ruan Yi-Run, Lao Song-Yang, Tang Jun, Bai Liang, Guo Yan-Ming. Node importance ranking method in complex network based on gravity method. Acta Physica Sinica, 2022, 71(17): 176401. doi: 10.7498/aps.71.20220565
[2]	Xu Ming, Xu Chuan-Yun, Cao Ke-Fei. Effect of degree correlations on controllability of undirected networks. Acta Physica Sinica, 2017, 66(2): 028901. doi: 10.7498/aps.66.028901
[3]	Su Zhen, Gao Chao, Li Xiang-Hua. Analysis of the effect of node centrality on diffusion mode in complex networks. Acta Physica Sinica, 2017, 66(12): 120201. doi: 10.7498/aps.66.120201
[4]	Ruan Yi-Run, Lao Song-Yang, Wang Jun-De, Bai Liang, Chen Li-Dong. Node importance measurement based on neighborhood similarity in complex network. Acta Physica Sinica, 2017, 66(3): 038902. doi: 10.7498/aps.66.038902
[5]	Hu Yao-Guang, Wang Sheng-Jun, Jin Tao, Qu Shi-Xian. Biased random walks in the scale-free networks with the disassortative degree correlation. Acta Physica Sinica, 2015, 64(2): 028901. doi: 10.7498/aps.64.028901
[6]	Min Lei, Liu Zhi, Tang Xiang-Yang, Chen Mao, Liu San-Ya. Evaluating influential spreaders in complex networks by extension of degree. Acta Physica Sinica, 2015, 64(8): 088901. doi: 10.7498/aps.64.088901
[7]	Duan Dong-Li, Zhan Ren-Jun. Evolution mechanism of node importance based on the information about cascading failures in complex networks. Acta Physica Sinica, 2014, 63(6): 068902. doi: 10.7498/aps.63.068902
[8]	Yuan Chao, Chai Yi. Group similarity based algorithm for network community structure detection. Acta Physica Sinica, 2012, 61(21): 218901. doi: 10.7498/aps.61.218901
[9]	Tian Li-Xin, He Ying-Huan, Huang Yi. A novel local-world-like evolving bipartite network model. Acta Physica Sinica, 2012, 61(22): 228903. doi: 10.7498/aps.61.228903
[10]	Zhang Cong, Shen Hui-Zhang, Li Feng, Yang He-Qun. Multi-resolution density modularity for finding community structure in complex networks. Acta Physica Sinica, 2012, 61(14): 148902. doi: 10.7498/aps.61.148902
[11]	Zhou Xuan, Zhang Feng-Ming, Li Ke-Wu, Hui Xiao-Bin, Wu Hu-Sheng. Finding vital node by node importance evaluation matrix in complex networks. Acta Physica Sinica, 2012, 61(5): 050201. doi: 10.7498/aps.61.050201
[12]	Tian Liu, Di Zeng-Ru, Yao Hong. Effect of distribution of weight on the efficiency of weighted networks. Acta Physica Sinica, 2011, 60(2): 028901. doi: 10.7498/aps.60.028901
[13]	Yan Xiao-Yong, Wang Ming-Sheng. Influence of growth speed on the actors’ degree distribution of collaboration networks. Acta Physica Sinica, 2010, 59(2): 851-858. doi: 10.7498/aps.59.851
[14]	Zhao Qing-Gui, Kong Xiang-Xing, Hou Zhen-Ting. The degree distribution of simple generalized collaboration networks. Acta Physica Sinica, 2009, 58(10): 6682-6685. doi: 10.7498/aps.58.6682
[15]	Guo Jin-Li. Impact of edges for new nodes on scale-free networks. Acta Physica Sinica, 2008, 57(2): 756-761. doi: 10.7498/aps.57.756
[16]	Guo Jin-Li, Wang Li-Na. Scale-free networks with the power-law exponent between 1 and 3. Acta Physica Sinica, 2007, 56(10): 5635-5639. doi: 10.7498/aps.56.5635
[17]	Yan Dong, Qi Guo-Ning. The scale-free feature and evolving model of large-scale software systems. Acta Physica Sinica, 2006, 55(8): 3799-3804. doi: 10.7498/aps.55.3799
[18]	Zhang Pei-Pei, He Yue, Zhou Tao, Su Bei-Bei, Chang Hui, Zhou Yue-Ping, Wang Bing-Hong, He Da-Ren. A model describing the degree distribution of collaboration networks. Acta Physica Sinica, 2006, 55(1): 60-67. doi: 10.7498/aps.55.60
[19]	Guo Jin-Li. The bilateral power-law distribution model of supply chain networks. Acta Physica Sinica, 2006, 55(8): 3916-3921. doi: 10.7498/aps.55.3916
[20]	Li Ying, Shan Xiu-Ming, Ren Yong. Average path length of Internet with power law degree distribution. Acta Physica Sinica, 2004, 53(11): 3695-3700. doi: 10.7498/aps.53.3695

Catalog

Vol. 62, Issue 20 - 2013-10-20

Metrics

Abstract views: 7545
PDF Downloads: 1354
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板