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Distance Measures for Dynamic Citation Networks

Physica A, Vol. 389, pp. 4201-4208, 2010

8 Pages Posted: 11 Sep 2009 Last revised: 9 Nov 2010

Michael James Bommarito II

LexPredict, LLC; Bommarito Consulting, LLC; Chicago-Kent College of Law - Illinois Institute of Technology; Michigan State College of Law

Daniel Martin Katz

Illinois Tech - Chicago Kent College of Law

Jon Zelner

University of Michigan at Ann Arbor - Center for Study of Complex Systems

James H. Fowler

UC San Diego Division of Social Sciences; UC San Diego School of Medicine

Date Written: September 11, 2009

Abstract

Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent a substantively important form of acyclic digraphs. 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 meaningful distance measures for these networks. We apply our sink based distance measure and the single-linkage hierarchical clustering algorithm to the first quarter century of decisions of the United States Supreme Court. Despite applying the simplest distance measure and a straight forward clustering algorithm, qualitative analysis reveals that accurate clusterings are produced by this scheme.

Keywords: citation networks, acyclic digraphs, dynamic network analysis, judicial citations, patent citations, distance measures, community detection, clustering

JEL Classification: C61, C63, C60, C88

Suggested Citation

Bommarito, Michael James and Katz, Daniel Martin and Zelner, Jon and Fowler, James H., Distance Measures for Dynamic Citation Networks (September 11, 2009). Physica A, Vol. 389, pp. 4201-4208, 2010. Available at SSRN: https://ssrn.com/abstract=1472037

Michael Bommarito

LexPredict, LLC ( email )

MI
United States

HOME PAGE: http://lexpredict.com

Bommarito Consulting, LLC ( email )

MI 48098
United States

HOME PAGE: http://bommaritollc.com

Chicago-Kent College of Law - Illinois Institute of Technology ( email )

565 W. Adams St.
Chicago, IL 60661-3691
United States

Michigan State College of Law ( email )

318 Law College Building
East Lansing, MI 48824-1300
United States

Daniel Katz (Contact Author)

Illinois Tech - Chicago Kent College of Law ( email )

565 W. Adams St.
Chicago, IL 60661-3691
United States

HOME PAGE: http://www.danielmartinkatz.com/

Jon Zelner

University of Michigan at Ann Arbor - Center for Study of Complex Systems ( email )

321A West Hall
Ann Arbor, MI 48109
United States

James Fowler

UC San Diego Division of Social Sciences ( email )

9500 Gilman Drive
Code 0521
La Jolla, CA 92093-0521
United States

HOME PAGE: http://jhfowler.ucsd.edu

UC San Diego School of Medicine ( email )

9500 Gilman Drive
MC 0507
La Jolla, CA 92093
United States

HOME PAGE: http://jhfowler.ucsd.edu

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