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Large-scale structure of time evolving citation networks

  • Interdisciplinary Physics
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Abstract.

In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers, patents, or court cases. We describe three different methods of analysis, one based on an expectation-maximization algorithm, one based on modularity optimization, and one based on eigenvector centrality. Using the network of citations between opinions of the United States Supreme Court as an example, we demonstrate how each of these methods can reveal significant structural divisions in the network and how, ultimately, the combination of all three can help us develop a coherent overall picture of the network's shape.

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References

  • R. Albert, A.L. Barabási, Reviews of Modern Physics 74, 47 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  • S.N. Dorogovtsev, J.F.F. Mendes, Advances in Physics 51, 1079 (2002)

    Article  ADS  Google Scholar 

  • M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • D.J.de S. Price, Science 149, 510 (1965)

    Article  ADS  Google Scholar 

  • D.J.de S. Price, J. Am. Soc. Inf. Sci. 27, 292 (1976)

    Article  Google Scholar 

  • L. Egghe, R. Rousseau, Introduction to Informetrics (Elsevier, Amsterdam, 1990)

  • A. Jaffe, M. Trajtenberg, Patents, Citations and Innovations: A Window on the Knowledge Economy (MIT Press, Cambridge, MA, 2002)

  • G. Clarkson, D. DeKorte, in Progress in Convergence: Technologies for Human Wellbeing, edited by W.S. Bainbridge, M.C. Roco (New York Academy of Sciences, 2006), Vol. 1093 of Annals of the New York Academy of Science, pp. 180–200

  • G. Csárdi, K.J. Strandburg, L. Zalanyi, J. Tobochnik, P. Érdi, Physica A 374, 783 (2007)

    Article  ADS  Google Scholar 

  • F.B. Cross, T.A. Smith, A. Tomarchio, Determinants of cohesion in the supreme court's network of precedents (2006), http://ssrn.com/abstract=924110

  • J.H. Fowler, T.R. Johnson, J.F. Spriggs II, S. Jeon, P.J. Wahlbeck, Political Analysis doi:10.1093/pan/mpm011 (in-press)

  • J.H. Fowler, S. Jeon, Social Networks doi:10.1016/j.socnet.2007.05.001 (2007)

  • P.O. Seglen, J. Am. Soc. Inf. Sci. 43, 628 (1992)

    Article  Google Scholar 

  • S. Redner, Eur. Phys. J. B 4, 131 (1998)

    Article  ADS  Google Scholar 

  • A.P. Dempster, N.M. Laird, D.B. Rubin, J. Roy. Stat. Soc. B 39, 1 (1977)

    MATH  MathSciNet  Google Scholar 

  • G.J. McLachlan, T. Krishnan, The EM Algorithm and Extensions (John Wiley & Sons, Inc., New York, 1997)

  • M.E.J. Newman, E.A. Leicht, Proc. Nat. Acad. Sci. USA 104, 9564 (2007)

    Article  Google Scholar 

  • H. Akaike, IEEE Trans. Auto. Control 19, 716 (1974)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • G. Schwarz, Annals of Statistics 6, 461 (1978)

    MATH  MathSciNet  Google Scholar 

  • M.E.J. Newman, Eur. Phys. J. B 38, 321 (2004)

    Article  ADS  Google Scholar 

  • L. Danon, J. Duch, A. Diaz-Guilera, A. Arenas, J. Stat. Mech. P09008 (2005)

  • M.E.J. Newman, Proc. Nat. Acad. Sci. USA 103, 8577 (2006)

    Article  ADS  Google Scholar 

  • M.E.J. Newman, M. Girvan, Phys. Rev. E 69, 026113 (2004)

    Article  ADS  Google Scholar 

  • M.E.J. Newman, Phys. Rev. E 69, 066133 (2004)

    Article  ADS  Google Scholar 

  • U. Brandes, D. Delling, M. Gaertler, R. Görke, M. Hoefer, Z. Nikoloski, D. Wagner, On Finding Graph Clusterings with Maximum Modularity, in Proceedings of the 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (Springer, Berlin, in press), Lecture Notes in Computer Science (in press)

  • A.E. Krause, K.A. Frank, D.M. Mason, R.E. Ulanowicz, W.W. Taylor, Nature 426, 282 (2003)

    Article  ADS  Google Scholar 

  • P.F. Bonacich, Am. J. Sociol. 92, 1170 (1987)

    Article  Google Scholar 

  • J.M. Kleinberg, J. ACM 46, 604 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • A.H. Kelly, W.A. Harbison, H. Belz, The American Constitution: Its origins and development, 7th edn. (Norton, New York, 1991)

  • M.I. Urofsky, P. Finkelman, A March of Liberty: A Constitutional History of the United States, 2nd edn. (Oxford University Press, New York, 2002)

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Leicht, E., Clarkson, G., Shedden, K. et al. Large-scale structure of time evolving citation networks. Eur. Phys. J. B 59, 75–83 (2007). https://doi.org/10.1140/epjb/e2007-00271-7

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