\'Etude de l'omnipr\'esence des propri\'et\'es petit- monde et sans-\'echelle

Abstract

The small-world and scale-free properties were identified in real-world complex net-works at the end of the 90s. Their analysis led to a better understanding of the dynamics and functioning of certain systems, and they were studied in many subsequent works. This might be the reason why one frequently finds, in the complex networks literature, assertions regarding their ubiquity, their validity for almost all complex networks. Yet, the mentioned seminal works were conducted on a very limited number of networks, and, to the best of our knowledge, no large-scale study has been conducted to answer this question. In this work, we take advantage, on the one hand, of the many datasets now available online, to constitute a large collection of networks, and on the other hand, of recent analysis tools, to check the validity of this hypothesis of ubiquity. It turns out a large majority of the studied networks are indeed small-world, how-ever this is not the case for the scale-free property, since the degree distribution of a significant proportion of our networks does not follow a power-law. MOTS-CL{\'E}S : R{\'e}seaux complexes, propri{\'e}t{\'e}s topologiques, petit-monde, sans-{\'e}chelle.