Distance Measures for Dynamic Citation Networks
Abstract
Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent an 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.