  We explore one aspect of the structure of a codified legal system at the
national level using a new type of representation to understand the strong or
weak dependencies between the various fields of law. In Part I of this study,
we analyze the graph associated with the network in which each French legal
code is a vertex and an edge is produced between two vertices when a code cites
another code at least one time. We show that this network distinguishes from
many other real networks from a high density, giving it a particular structure
that we call concentrated world and that differentiates a national legal system
(as considered with a resolution at the code level) from small-world graphs
identified in many social networks. Our analysis then shows that a few
communities (groups of highly wired vertices) of codes covering large domains
of regulation are structuring the whole system. Indeed we mainly find a central
group of influent codes, a group of codes related to social issues and a group
of codes dealing with territories and natural resources. The study of this
codified legal system is also of interest in the field of the analysis of real
networks. In particular we examine the impact of the high density on the
structural characteristics of the graph and on the ways communities are
searched for. Finally we provide an original visualization of this graph on an
hemicyle-like plot, this representation being based on a statistical reduction
of dissimilarity measures between vertices. In Part II (a following paper) we
show how the consideration of the weights attributed to each edge in the
network in proportion to the number of citations between two vertices (codes)
allows deepening the analysis of the French legal system.
