Characterization of Spatial Networks

Orateur : Marc BARTHELEMY (Labo. Physique Théorique, CEA, Gif/Yvette)

Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, vascular and neural networks, are all examples where space is relevant and where topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of these "spatial networks" is thus crucial for many different fields ranging from urbanism to biology and epidemiology. An important consequence of space on networks is that there is a cost associated to the length of edges which in turn has dramatic effects on their topological structure : due to physical constraints, most standard measures for complex networks are irrelevant for this class of graphs and I will review here some of the most interesting and promising measures for characterizing these graphs and their time evolution. In particular, I will illustrate on various real-world examples the simplicity profile, the spatial distribution of the betweenness centrality and, if time allows, the shape distribution of faces. I will end this talk by discussing briefly interesting directions for modelling these systems.

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