Abstract

Unlike usual real graphs which have a low number of edges, we study here a dense network constructed from legal citations. This study is achieved on the simple graph and on the multiple graph associated to this legal network, this allows exploring the behavior of the network structural properties and communities by considering the weighted graph and see which additional information are provided by the weights. We propose new measures to assess the role of the weights in the network structure and to appreciate the weights repartition. Then we compare the communities obtained on the simple graph and on the weighted graph. We also extend to weighted networks the amphitheater-like representation of this legal network. Finally we evaluate the robustness of our measures and methods thus taking into account potential errors which may occur by getting data or building the network. Our methodology may open new perspectives in the analysis of weighted networks.