Journal of the Korea Society of Computer and Information (한국컴퓨터정보학회논문지)

Korean Society of Computer Information (한국컴퓨터정보학회)
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Analysis of Effect of an Additional Edge on Eigenvector Centrality of Graph

  • Received : 2015.08.07
  • Accepted : 2016.01.06
  • Published : 2016.01.30
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Abstract

There are many methods to describe the importance of a node, centrality, in a graph. In this paper, we focus on the eigenvector centrality. In this paper, an analytical method to estimate the difference of centrality with an additional edge in a graph is proposed. In order to validate the analytical method to estimate the centrality, two problems, to decide an additional edge that maximizes the difference of all centralities of all nodes in the graph and to decide an additional edge that maximizes the centrality of a specific node, are solved using three kinds of random graphs and the results of the estimated edge and observed edge are compared. Though the estimated centrality difference is slightly different from the observed real centrality in some cases, it is shown that the proposed method is effective to estimate the centrality difference with a short running time.

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References

  1. P. Boldi and S. Vigna, "Axioms for Centrality", Social and Information Networks, Nov. 2013.
  2. R. Lempel and S. Moran, "Rank-Stability and Rank-Similarity of Link-Based Web Ranking Algorithms in Authority-Connected Graphs", Information Retrieval, Vol. 8, No. 2, pp 245-264, 2005. https://doi.org/10.1007/s10791-005-5661-0
  3. K. Avrachenkov and N. Litvak, "The Effect of New Links on Google Pagerank, Stochastic Models", 22 (2), pp. 319-331, 2006. https://doi.org/10.1080/15326340600649052
  4. J. Ronqui and T. Gonzalo, "Analyzing Complex Networks Through Correlations in Centrality Measurements", Social and Information Networks, June 2014.
  5. S. Borgatti, K. Carley and D. Krackhardt, "On the Robustness of Centrality Measures under Conditions of Imperfect Data", Social Networks 28.2, pp.124-136, 2006. https://doi.org/10.1016/j.socnet.2005.05.001
  6. S. Segarra and A. Ribeiro, "Stability and Continuity of Centrality Measures in Weighted Graphs", Social and Information Networks, Oct. 2014.
  7. T. Chartier, E. Kreutzer, A. Langville, and K. Pedings, "Sensitivity and Stability of Ranking Vectors", SIAM J. Sci. Comput., 33(3), pp. 1077-1102, 2011. https://doi.org/10.1137/090772745
  8. A. Ng, A. Zheng and M. Jordan, "Stable Algorithms for Link Analysis", SIGIR '01 Proceedings of the 24th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 258-266, 2001.
  9. C. Correa and K. Ma, "Visual Reasoning about Social Networks using Centrality Sensitivity", IEEE Transactions on Visualization and Computer Graphics, Vol. 18, No. 1, pp. 106-120, 2012. https://doi.org/10.1109/TVCG.2010.260
  10. G. Golub and C. Loan, "Matrix Computations", Johns Hopkins, 1988.
  11. P. Erdos and A. Renyi, "On Random Graphs, I", Publicationes Mathematicae 6, pp. 290-297, 1959.
  12. A.-L. Barabasi and R. Albert, "Emergence of Scaling in Random Networks", Science, 286, pp. 509-512, 1997.
  13. D. Watts and S. Strogatz, "Collective Dynamics of 'Small-World' Networks", Nature 393 (6684), pp. 440-442. 1998. https://doi.org/10.1038/30918
  14. Woo-Key Lee, "Detecting Intentionally Biased Web Pages In terms of Hypertext Information", Journal of The Korea Society of Computer and Information, Vol. 10, No. 1, pp.59-66, 2005.
  15. Sang-Un Lee, "Maximum Degree Vertex Central Located Algorithm for Bandwidth Minimization Problem", Journal of The Korea Society of Computer and Information, Vol. 20, No. 7, pp.41-47, 2015. https://doi.org/10.9708/jksci.2015.20.7.041