On Merging and Dividing Social Graphs

  • 1 Department of Knowledge Processing and Language Engineering Faculty of Computer Science, Otto von Guericke University Magdeburg Universitaetsplatz 2, 39106 Magdeburg, Germany

Abstract

Modeling social interaction can be based on graphs. However most models lack the flexibility of including larger changes over time. The Barabási-Albert-model is a generative model which already offers mechanisms for adding nodes. We will extent this by presenting four methods for merging and five for dividing graphs based on the Barabási- Albert-model. Our algorithms were motivated by different real world scenarios and focus on preserving graph properties derived from these scenarios. With little alterations in the parameter estimation those algorithms can be used for other graph models as well. All algorithms were tested in multiple experiments using graphs based on the Barabási- Albert-model, an extended version of the Barabási-Albert-model by Holme and Kim, the Watts-Strogatz-model and the Erdős-Rényi-model. Furthermore we concluded that our algorithms are able to preserve different properties of graphs independently from the used model. To support the choice of algorithm, we created a guideline which highlights advantages and disadvantages of discussed methods and their possible use-cases.

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  • [1] P. ErdÃűs and A. RÃl’nyi, “On random graphs, i,” Publicationes Mathematicae (Debrecen), vol. 6, pp. 290-297, 1959.

  • [2] D. J. Watts and S. H. Strogatz, “Collective dynamics of â˘AŸsmall-worldâ˘A ´Z networks,” Nature, vol. 393, no. 6684, pp. 440-442, Jun. 1998.

  • [3] A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” science, vol. 286, no. 5439, pp. 509-512, 1999.

  • [4] R. Albert, H. Jeong, and A.-L. Barabasi, “The diameter of the world wide web,” Nature, vol. 401, no. 6749, pp. 130-131, Sep. 1999, arXiv:condmat/ 9907038.

  • [5] R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins, “Extracting large-scale knowledge bases from the web,” in Proceedings of the 25th VLDB Conference, 1999, p. 639â˘A ¸S650.

  • [6] A.-L. Barabasi, R. Albert, and H. Jeong, “Meanfield theory for scale-free random networks,” Physica A: Statistical Mechanics and its Applications, vol. 272, no. 1-2, pp. 173-187, Oct. 1999, arXiv:cond-mat/9907068.

  • [7] W. Zachary, “An information flow model for conflict and fission in small groups,” Journal of Anthropological Research, vol. 33, pp. 452-473, 1977.

  • [8] P. Held, A. Dockhorn, and R. Kruse, “On merging and dividing of barabasi-albert-graphs,” in Evolving and Autonomous Learning Systems (EALS), 2014 IEEE Symposium on. IEEE, Dec. 2014, pp. 17-24.

  • [9] P. Holme and B. J. Kim, “Growing scale-free networks with tunable clustering,” Physical review E, vol. 65, no. 2, p. 026107, 2002.

  • [10] G. Bianconi and A.-l. BarabÃa˛si, “Competition and multiscaling in evolving networks,” Europhysics Letters, vol. 54, p. 436â˘A ¸S442, May 2001.

  • [11] E. N. Gilbert, “Random graphs,” The Annals of Mathematical Statistics, pp. 1141-1144, 1959.

  • [12] R. Kruse, C. Borgelt, F. Klawonn, C. Moewes, M. Steinbrecher, and P. Held, Computational Intelligence: A Methodological Introduction, ser. Texts in Computer Science. New York: Springer, 2013.

  • [13] D. Zwillinger and S. Kokoska, CRC standard probability and statistics tables and formulae. CRC Press, 1999.

  • [14] M. G. Kendall, “A new measure of rank correlation,” Biometrika, vol. 30, no. 1-2, pp. 81-93, 1938.

  • [15] P. Held, A. Dockhorn, and R. Kruse, “Generating events for dynamic social network simulations,” in Proceedings of 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, ser. Communications in Computer and Information Science, A. Laurent, O. Strauss, B. Bouchon-Meunier, and R. R. Yager, Eds. Switzerland: Springer International Publishing, 2014, pp. 46-55.

  • [16] P. Held, C. Moewes, C. Braune, R. Kruse, and B. A. Sabel, “Advanced analysis of dynamic graphs in social and neural networks,” in Towards Advanced Data Analysis by Combining Soft Computing and Statistics, ser. Studies in Fuzziness and Soft Computing, C. Borgelt, M. Á. Gil, J. M. C. Sousa, and M. Verleysen, Eds. Berlin Heidelberg: Springer, 2013, vol. 285, pp. 205-222.

  • [17] P. Held and R. Kruse, “Analysis and visualization of dynamic clusterings,” in 2013 46th Hawaii International Conference on System Sciences. Los Alamitos, CA, USA: IEEE Computer Society, Jan. 2013, pp. 1385-1393.

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