Properties of the United States Code Citation Network
4 Pages Posted: 10 Nov 2009 Last revised: 24 Mar 2010
Date Written: November 9, 2009
The United States Code (Code) is an important source of Federal law that is produced by the interactions of many heterogeneous actors in a complex, dynamic space. The Code can be represented as the union of a hierarchical network and a citation network over the vertices representing the language of the Code. In this paper, we investigate the properties of the Code’s citation network by examining the directed degree distributions of the network. We ﬁnd that the power-law model is a plausible ﬁt for the outdegree distribution but not for the indegree distribution. In order to better understand this result, we construct a model with the assumption that the probability of citation is a per-word rate. We calculate the adjusted degree of each vertex under this model and study the directed adjusted degree distributions. These adjusted degree distributions indicate that both the adjusted indegree and outdegree distributions seems to follow a log-normal form, not a power-law form. Our ﬁndings indicate that the power-law is not generally applicable to degree distributions within the United States Code but that the distribution of degree per word is well-described by a log-normal model.
Keywords: United States Code, Citation Network, Computational Legal Studies, Skewed Distributions, Degree Distribution, Power Laws
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