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Analyzing the Structure and Evolution of Massive Telecom Graphs
May 2008 (vol. 20 no. 5)
pp. 703-718
With ever growing competition in telecommunications markets, operators have to increasingly rely on business intelligence to offer the right incentives to their customers. Existing approaches for telecom business intelligence have almost solely focused on the individual behavior of customers. In this paper, we use the Call Detail Records of a mobile operator to construct Call graphs, that is, graphs induced by people calling each other. We determine the structural properties of these graphs and also introduce the {\sl Treasure-Hunt} model to describe the shape of mobile call graphs. We also determine how the structure of these call graphs evolve over time. Finally, since Short Messaging Service (SMS) is becoming a preferred mode of communication among many sections of the society we also study the properties of the SMS graph. Our analysis indicates several interesting similarities as well as differences between the SMS graph and the corresponding call graph. We believe that our analysis techniques can allow telecom operators to better understand the social behavior of their customers, and potentially provide major insights for designing effective incentives.

[1] J. Abello, P.M. Pardalos, and M.G.C. Resende, “On Maximum Clique Problems in Very Large Graphs,” DIMACS Series External Memory Algorithms, J. Abello and J. Vitter, eds., Am. Math. Soc., pp. 119-130, 1999.
[2] W. Aiello, F. Chung, and L. Lu, “A Random Graph Model for Massive Graphs,” Proc. 32nd Ann. ACM Symp. Theory of Computing (STOC '00), pp. 171-180, May 2000.
[3] W.H.A. Chan and K.C.C. Xin Yao, “A Novel Evolutionary Data Mining Algorithm with Applications to Churn Prediction,” IEEE Trans. Evolutionary Computation, vol. 7, no. 6, pp. 532-545, Dec. 2003.
[4] A.L. Barabasi and R. Albert, “Emergence of Scaling in Random Networks,” Science, vol. 286, pp. 509-512, Oct. 1999.
[5] S. Brin and L. Page, “The Anatomy of a Large-Scale Hypertextual Web Search Engine,” Computer Networks and ISDN Systems, vol. 30, nos. 1-7, pp. 107-117, 1998.
[6] A.Z. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, and J.L. Wiener, “Graph Structure in the Web,” Computer Networks, vol. 33, pp. 309-320, 2000.
[7] G. Caldarelli, Scale-Free Networks. Oxford Univ. Press, 2007.
[8] S. Carmi, S. Havlin, S. Kirkpatrick, Y. Shavitt, and E. Shir, “MEDUSA: New Model of Internet Topology Using $k\hbox{-}{\rm Shell}$ Decomposition,” Proc. Int'l Workshop and Conf. Network Science (NetSci), 2006.
[9] W. de Nooy, A. Mrvar, and V. Batagelj, Exploratory Social Network Analysis with Pajek. Cambridge Univ. Press, 2005.
[10] D. Donato, L. Laura, S. Leonardi, and S. Millozzi, “Large-Scale Properties of the Webgraph,” The European Physical J. B, vol. 38, pp. 239-243, 2004.
[11] D. Donato, S. Leonardi, S. Millozzi, and P. Tsaparas, “Mining the Inner Structure of the Web Graph,” Proc. Eighth Int'l Workshop Web and Databases (WebDB), 2005.
[12] S. Dorogovtsev and J. Mendes, Evolution of Networks: From Biological Nets to the Internet and the WWW. Oxford Univ. Press, 2000.
[13] T. Euler, “Churn Prediction in Telecommunications Using MiningMart,” Proc. First Workshop Data Mining and Business (DMBiz), 2005.
[14] M. Faloutsos, P. Faloutsos, and C. Faloutsos, “On Power-Law Relationships of the Internet Topology,” Proc. ACM SIGCOMM '99, pp. 251-262, 1999.
[15] J. Kleinberg, “Authoritative Sources in a Hyperlinked Environment,” J. ACM, vol. 46, 1999.
[16] R. Kumar, J. Novak, P. Raghavan, and A. Tomkins, “Structure and Evolution of Blogspace,” Comm. ACM, vol. 47, no. 12, pp. 35-39, 2004.
[17] R. Kumar, J. Novak, and A. Tomkins, “Structure and Evolution of Online Social Networks,” Proc. ACM SIGKDD, 2006.
[18] R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins, “Trawling the Web for Emerging Cyber-Communities,” Proc. Eighth Int'l Conf. World Wide Web (WWW '99), pp. 1481-1493, 1999.
[19] J. Leskovec, J. Kleinberg, and C. Faloutsos, “Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations,” Proc. ACM SIGKDD '05, pp. 177-187, 2005.
[20] D. Liben-Nowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins, “Geographic Routing in Social Networks,” Proc. Nat'l Academy of Sciences, vol. 102, no. 33, pp. 11623-11628, 2005.
[21] A.A. Nanavati, S. Gurumurthy, G. Das, D. Chakraborty, K. Dasgupta, S. Mukherjea, and A. Joshi, “On the Structural Properties of Massive Telecom Call Graphs: Findings and Implications,” Proc. 15th ACM Conf. Information and Knowledge Management (CIKM), 2006.
[22] M.E.J. Newman, “The Structure and Function of Complex Networks,” SIAM Rev., vol. 45, p. 167, 2003.
[23] A. Ntoulas, J. Cho, and C. Olston, “What's New on the Web? The Evolution of Web from a Search Engine Perspective,” Proc. 13th Int'l Conf. World Wide Web (WWW '04), pp. 1-12, 2004.
[24] C.R. Palmer, P.B. Gibbons, and C. Faloutsos, “ANF: A Fast and Scalable Tool for Data Mining in Massive Graphs,” Proc. ACM SIGKDD '02, pp. 81-90, 2002.
[25] G. Siganos, S. Tauro, and M. Faloutsos, “Jellyfish: A Conceptual Model for the AS Internet Topology,” J. Comm. and Networks, vol. 8, no. 3, pp. 339-350, Sept. 2006.

Index Terms:
Data mining Database Applications, Database Management, Information Technology and Systems, Graph algorithms, Telecom Call Graphs, Social Network Analysis
Amit Anil Nanavati, Rahul Singh, Dipanjan Chakraborty, Koustuv Dasgupta, Sougata Mukherjea, Gautam Das, Siva Gurumurthy, Anupam Joshi, "Analyzing the Structure and Evolution of Massive Telecom Graphs," IEEE Transactions on Knowledge and Data Engineering, vol. 20, no. 5, pp. 703-718, May 2008, doi:10.1109/TKDE.2007.190733
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