We perform a detailed analysis of the network constituted by the citations in a legal code, we search for hidden structures and properties. The graph associated to the Environmental code has a small-world structure and it is partitioned in several hidden communities of articles that only partially coincide with the organization of the code as given by its table of content. Several articles are also connected with a low number of articles but are intermediate between large communities. The structure of the Environmental Code is contrasting with the reference network of all the French Legal Codes that presents a rich-club of ten codes very central to the whole French legal system, but no small-world property. This comparison shows that the structural properties of the reference network associated to a legal system strongly depends on the scale and granularity of the analysis, as is the case for many complex systems
In recent years, the debates about the legal complexity by spontaneous orders and the possibility to control it have recovered strength and interest from many different scientific and politic communities. In particular, when it is seen as a part of liberalization, the simplification of law is expected by different governmental bodies in Europe to reduce some administrative burdens, to induce net positive economical returns or, for example, to increase the trade volumes between State members, or even worldwide. However, what is the legal complexity, how to control it, and what might be the impacts of the simplification of the Law, are questions without any element of answer. This article does not attempt to define or redefine legal complexity (exposed for instance by Hayekʼs works) but is aimed to better understand an aspect of this legal complexity induced by the numerous citation links between articles. In a seminal paper [1], we proposed to open a field of research aiming at building rigorous definitions of legal complexity that could be operational and exploited over large legal data bases.
Instead of directly confronting ourselves with the semantic complexity of the Law, we decided to analyze some structure associated with the legal systems. The positive fact in choosing this less ambitious objective is that we start building and using definitions of some aspects of legal complexity that, exploited with legal corpuses, provide new insight on the structural properties of some legal systems. These insights in turn open new perspectives on the Law. In particular the granularity of the legal texts we are considering is fundamental in the analysis because, as we shall see, the properties of the legal structure differ with the scale of the analysis (as is the case for many complex systems). Indeed in a previous study, we considered as the smallest object legal codes themselves and proceed to the analysis of the network formed by their cross-citations [2]. Using mathematical tools developed for the analysis of social networks, we found that several hidden stable structures are underlying the network of the French legal codes: a “rich club” is gathering the ten most cited and most citing codes that are very strongly connected to each others. Several other code communities also exist, in particular one of 12 codes related to “social matters” and “social activities”, and another one of 11 codes regulating various matters linked to “territories and natural resources”.
Changing the scale and granularity of the analysis, new structural properties are likely to appear. Here we choose to consider a single code and to analyze the network of citations within it. In a previous study, we have increased our resolution till the distinction of subdivisions within the articles. A statistical analysis of the distribution of the levels of organization of the Environmental Code and of the corresponding number of objects brought interesting clues about a kind of self-organization even within a code [3]. In the present study we go beyond the statistical analysis by considering with scrutiny the associated network structure.
Studying legal networks brings a new point of view on the issues of the complexity of Law. Approaching the complexity of the law through network analysis is a novel area of study and few analyses have been made so far.
Previous work mainly focused on the analysis of the citation network of the Supreme Court jurisprudence [4], [5], [6]. In [6], some structural elements are highlighted: the network possesses a main core of 122 vertices, the most cited cases and the most central cases are enumerated and, despite a low density, the network is locally dense. James Fowler also used the different notions of centrality to study the citation network of the Supreme Court precedents [4]. The United States Code is also considered as a network in [7], the vertices of the network are the different sections of the US Code and the links are citations links. A common aspect of these papers is the examination of the degree 1 distribution in order to bring out a scale-free effect. The network structure of the Uniform Commercial Code is analyzed in [8]; in this paper citations links and hierarchical links are considered and several tools are exposed in order to understand the shape of the network. These tools are computing indices of the graph (like small world indices or centralities) or performing a good visualization of the graph in order to detect communities.
In the next subsection we shall introduce the legal network we study throughout this paper and then in Section 3 we shall not only compute the degree distribution and central vertices but also exhibit a small-world structure and cluster the network into communities. The 1 The degree of a vertex is the number of vertices linked to this vertex.
analyses we perform, with an emphasis on legal interpretations of our results, will give us a better understanding of the sh
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