Dimensions fractales de réseaux vectoriels: Méthodes d'estimation et robustesse des résultats

Stream s networks are part of transport networks and m ore generally of "spatial networks" that gave rise to fundam ental researchs (Barthelemy, 2011) and applied geography (Strano et al., 2012). Numerous studies have focused on fractal analysis of stream networks. However, only few papers compare or discuss the estimation methods and the uncertainty of the main fractal indicator, the fractaldimension. This work focuses on the fractal properties of vector networks both virtual and actual. We first mention the essential distinction between infinite mathematical fractal and nature fractal. Then, we present different theoretical and em pirical dim ensions that we use. In particular, we com pare three fractal dim ensionestimators: the most classical estimator for stream networks, based on a topological approach with the Horton-Strahler ratios, and two other estimators based on a geometric approach, the box-counting dim ension and the correlation dimension. Three main methodological results can be highlighted: 1 - the study of virtual network contributes to the assessm ent of the various estimators relevance, according to the characteristics of networks; 2 - an empirical fractal domain must be determ ined with an objective method to estimate fractal dimensions that can be com pared; 3 - the observation of uncertainty and stability of the fractal dimension is necessary for anyvalid comparison.