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Distance measures for dynamic citation networks

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  • Bommarito, Michael J.
  • Katz, Daniel Martin
  • Zelner, Jonathan L.
  • Fowler, James H.

Abstract

Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent an important type of acyclic digraph. For example, the study of such networks includes the spread of ideas through academic citations, the spread of innovation through patent citations, and the development of precedent in common law systems. The specific dynamics that produce such acyclic digraphs not only differentiate them from other classes of graphs, but also provide guidance for the development of meaningful distance measures. In this article, we develop and apply our sink distance measure together with the single-linkage hierarchical clustering algorithm to both a two-dimensional directed preferential attachment model as well as empirical data drawn from the first quarter-century of decisions of the United States Supreme Court. Despite applying the simplest combination of distance measure and clustering algorithm, analysis reveals that more accurate and more interpretable clusterings are produced by this scheme.

Suggested Citation

  • Bommarito, Michael J. & Katz, Daniel Martin & Zelner, Jonathan L. & Fowler, James H., 2010. "Distance measures for dynamic citation networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(19), pages 4201-4208.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:19:p:4201-4208
    DOI: 10.1016/j.physa.2010.06.003
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    References listed on IDEAS

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    1. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    2. Fowler, James H. & Johnson, Timothy R. & Spriggs, James F. & Jeon, Sangick & Wahlbeck, Paul J., 2007. "Network Analysis and the Law: Measuring the Legal Importance of Precedents at the U.S. Supreme Court," Political Analysis, Cambridge University Press, vol. 15(3), pages 324-346, July.
    3. James H. Fowler & Dag W. Aksnes, 2007. "Does self-citation pay?," Scientometrics, Springer;Akadémiai Kiadó, vol. 72(3), pages 427-437, September.
    4. E. A. Leicht & G. Clarkson & K. Shedden & M. E.J. Newman, 2007. "Large-scale structure of time evolving citation networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 59(1), pages 75-83, September.
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    Citations

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    Cited by:

    1. Justin Stoler & Alessandria San Roman, 2016. "Where is precedent set? An exploratory geovisualization of State Supreme Court cases," Journal of Maps, Taylor & Francis Journals, vol. 12(2), pages 334-343, March.
    2. Shen, Yi, 2013. "Detect local communities in networks with an outside rate coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2821-2829.
    3. Clough, James R. & Evans, Tim S., 2016. "What is the dimension of citation space?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 235-247.

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